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Journal articles on the topic 'Fractional mean value theorem'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

GUO, PENG, CHANGPIN LI, and GUANRONG CHEN. "ON THE FRACTIONAL MEAN-VALUE THEOREM." International Journal of Bifurcation and Chaos 22, no. 05 (2012): 1250104. http://dx.doi.org/10.1142/s0218127412501040.

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In this paper, we derive a fractional mean-value theorem both in the sense of Riemann–Liouville and in the sense of Caputo. This new formulation is more general than the generalized Taylor's formula of Kolwankar and the fractional mean-value theorem in the sense of Riemann–Liouville developed by Trujillo.

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2

Zine, Houssine, El Mehdi Lotfi, Delfim F. M. Torres, and Noura Yousfi. "Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels." Axioms 11, no. 5 (2022): 231. http://dx.doi.org/10.3390/axioms11050231.

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We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives.

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3

Cheng, Jinfa. "On Multivariate Fractional Taylor’s and Cauchy’ Mean Value Theorem." Journal of Mathematical Study 52, no. 1 (2019): 38–52. http://dx.doi.org/10.4208/jms.v52n1.19.04.

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4

Chii-Huei, Yu. "Study on Some Properties of Fractional Analytic Function." International Journal of Mechanical and Industrial Technology 10, no. 1 (2022): 31–35. https://doi.org/10.5281/zenodo.7016567.

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<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional derivative, we study some properties of fractional analytic function, such as fractional Taylor’s theorem, first fractional derivative test, and second fractional derivative test. The major methods used in this paper are fractional Rolle’s theorem, fractional mean value theorem, product rule for fractional derivatives, and a new multiplication of fractional analytic functions. In fact, these new results are generalizations of those results in ordinary calculus. <strong>Key

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5

San, Mufit, and Seyma Ramazan. "A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity." Electronic Research Archive 32, no. 5 (2024): 3092–112. http://dx.doi.org/10.3934/era.2024141.

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<abstract><p>In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.</p></abstract>

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6

Gholizadeh Zivlaei, Leila, and Angelo B. Mingarelli. "On the Basic Theory of Some Generalized and Fractional Derivatives." Fractal and Fractional 6, no. 11 (2022): 672. http://dx.doi.org/10.3390/fractalfract6110672.

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We continue the development of the basic theory of generalized derivatives as introduced and give some of their applications. In particular, we formulate necessary conditions for extrema, Rolle’s theorem, the mean value theorem, the fundamental theorem of calculus, integration by parts, along with an existence and uniqueness theorem for a generalized Riccati equation, each of which provides simple proofs of the corresponding version for the so-called conformable fractional derivatives considered by many. Finally, we show that for each α>1 there is a fractional derivative and a corresponding

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7

Ramzi, B. Albadarneh, M. Batiha Iqbal, Adwai Ahmad, Tahat Nedal, and Alomari A.K. "Numerical approach of riemann-liouville fractional derivative operator." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 6 (2021): 5367–78. https://doi.org/10.11591/ijece.v11i6.pp5367-5378.

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This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating the Riemann-Liouville fractional derivative operator. These formulas are derived by utilizing some of forthright computations, and by utilizing the so-called weighted mean value theorem (WMVT). Undoubtedly, such formulas will be extremely useful in establishing new approaches for several solutions of both linear and nonlinear fractionalorder differential equations. This assertion is confirmed by addressing several linear and nonlinear

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8

Hadhoud, Adel R., Faisal E. Abd Alaal, Ayman A. Abdelaziz, and Taha Radwan. "Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination." Demonstratio Mathematica 54, no. 1 (2021): 436–51. http://dx.doi.org/10.1515/dema-2021-0040.

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Abstract In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduc

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9

Hasanah, Dahliatul. "On continuity properties of the improved conformable fractional derivatives." Jurnal Fourier 11, no. 2 (2022): 88–96. http://dx.doi.org/10.14421/fourier.2022.112.88-96.

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The conformable fractional derivative has been introduced to extend the familiar limit definition of the classical derivative. Despite having many advantages compared to other fractional derivatives such as satisfying nice properties as classical derivative and easy to solve numerically, it also has disadvantages as it gives large error compared to Riemann-Liouville and Caputo fractional derivatives. Modified types of conformable derivatives have been proposed to overcome the shortcoming. The improved conformal fractional derivatives are declared to be better approximations of Riemann-Liouvill

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10

Nwaeze, Eze R. "A Mean Value Theorem for the Conformable Fractional Calculus on Arbitrary Time Scales." Progress in Fractional Differentiation and Applications 2, no. 4 (2016): 287–91. http://dx.doi.org/10.18576/pfda/020406.

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11

Kajouni, Ahmed, Ahmed Chafiki, Khalid Hilal, and Mohamed Oukessou. "A New Conformable Fractional Derivative and Applications." International Journal of Differential Equations 2021 (November 26, 2021): 1–5. http://dx.doi.org/10.1155/2021/6245435.

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This paper is motivated by some papers treating the fractional derivatives. We introduce a new definition of fractional derivative which obeys classical properties including linearity, product rule, quotient rule, power rule, chain rule, Rolle’s theorem, and the mean value theorem. The definition D α f t = lim h ⟶ 0 f t + h e α − 1 t − f t / h , for all t > 0 , and α ∈ 0,1 . If α = 0 , this definition coincides to the classical definition of the first order of the function f .

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12

Wu, Shanhe, Muhammad Adil Khan, and Hidayat Ullah Haleemzai. "Refinements of Majorization Inequality Involving Convex Functions via Taylor’s Theorem with Mean Value form of the Remainder." Mathematics 7, no. 8 (2019): 663. http://dx.doi.org/10.3390/math7080663.

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The aim of this paper is to establish some refined versions of majorization inequality involving twice differentiable convex functions by using Taylor theorem with mean-value form of the remainder. Our results improve several results obtained in earlier literatures. As an application, the result is used for deriving a new fractional inequality.

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13

Ma, Li, Chengch ng Liu, Rui in Liu, Bo Wang, and Yix an Zhu. "On fractional mean value theorems associated with Hadamard fractional calculus and application." Fractional Differential Calculus, no. 2 (2020): 225–36. http://dx.doi.org/10.7153/fdc-2020-10-14.

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14

Wooley, Trevor. "The application of a new mean value theorem to the fractional parts of polynomials." Acta Arithmetica 65, no. 2 (1993): 163–79. http://dx.doi.org/10.4064/aa-65-2-163-179.

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15

Atici, Ferhan, and Meltem Uyanik. "Analysis of discrete fractional operators." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 139–49. http://dx.doi.org/10.2298/aadm150218007a.

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In this paper, we introduce two new monotonicity concepts for a nonnegative or nonpositive valued function defined on a discrete domain. We give examples to illustrate connections between these new monotonicity concepts and the traditional ones. We then prove some monotonicity criteria based on the sign of the fractional difference operator of a function f, ??f with 0 < ? < 1. As an application, we state and prove the mean value theorem on discrete fractional calculus.

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16

Martínez, Francisco, and Mohammed K. A. Kaabar. "A New Generalized Definition of Fractal–Fractional Derivative with Some Applications." Mathematical and Computational Applications 29, no. 3 (2024): 31. http://dx.doi.org/10.3390/mca29030031.

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In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function’s derivative. We complete the theory of generalized FF calculus by proposing a notion of integr

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17

Martínez, Francisco, and Mohammed K. A. Kaabar. "A Novel Theoretical Investigation of the Abu-Shady–Kaabar Fractional Derivative as a Modeling Tool for Science and Engineering." Computational and Mathematical Methods in Medicine 2022 (September 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/4119082.

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A newly proposed generalized formulation of the fractional derivative, known as Abu-Shady–Kaabar fractional derivative, is investigated for solving fractional differential equations in a simple way. Novel results on this generalized definition is proposed and verified, which complete the theory introduced so far. In particular, the chain rule, some important properties derived from the mean value theorem, and the derivation of the inverse function are established in this context. Finally, we apply the results obtained to the derivation of the implicitly defined and parametrically defined funct

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18

Mohammed, Pshtiwan Othman, Thabet Abdeljawad, and Faraidun Kadir Hamasalh. "On Discrete Delta Caputo–Fabrizio Fractional Operators and Monotonicity Analysis." Fractal and Fractional 5, no. 3 (2021): 116. http://dx.doi.org/10.3390/fractalfract5030116.

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The discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale Z. Moreover, the action of Q− operator and discrete delta Laplace transform method are also reported. Furthermore, a relationship between the discrete delta Caputo-Fabrizio-Caputo and Caputo-Fabrizio-Riemann fractional differences is also studied in detail. To better understand the dynamic behavior of the obtained monotonicity results, the fractional difference mean value theorem is derived. The idea used in

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19

Nabil, Tamer. "Solvability of Fractional Differential Inclusion with a Generalized Caputo Derivative." Journal of Function Spaces 2020 (December 26, 2020): 1–11. http://dx.doi.org/10.1155/2020/2917306.

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This paper is devoted to the investigation of a kind of generalized Caputo semilinear fractional differential inclusions with deviated-advanced nonlocal conditions. Solvability of the problem is established by means of the Leray-Schauder’s alternative approach with the help of the Lagrange mean-value classical theorem. Finally, some examples are given to delineate the efficient of theoretical results.

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20

Mohammed, Pshtiwan Othman, Christopher S. Goodrich, Aram Bahroz Brzo, Dumitru Baleanu, and Yasser S. Hamed. "New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel." Mathematical Biosciences and Engineering 19, no. 4 (2022): 4062–74. http://dx.doi.org/10.3934/mbe.2022186.

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<abstract><p>This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The $ \nu- $monotonicity definitions, namely $ \nu- $(strictly) increasing and $ \nu- $(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with $ \nu- $monotonicity definitions, we find that the investigated discrete fractional operators will be $ \nu^2- $(strictly) increasing or $ \nu^2- $(strictly) decreasing in certain domains of the time scale $ \mathbb{N}_a: = \{a, a

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21

Huang, Chun Miao, and Wu Sheng Wang. "Estimation of Unknown Function in a Class of Singular Difference Inequality in Engineering." Advanced Materials Research 945-949 (June 2014): 2467–70. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.2467.

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In this paper, we discuss a class of new weakly singular difference inequality, which is solved using change of variable, discrete Jensen inequality, Beta function, the mean-value theorem for integrals and amplification method, and explicit bounds for the unknown functions is given clearly. The derived results can be applied in the study of fractional difference equations in Engineering.

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22

Wang, Wu Sheng, and Zong Yi Hou. "A Class of Nonlinear Singular Difference Inequality in Engineering." Applied Mechanics and Materials 577 (July 2014): 824–27. http://dx.doi.org/10.4028/www.scientific.net/amm.577.824.

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In this paper, we discuss a class of new nonlinear weakly singular difference inequality. Using change of variable, discrete Jensen inequality, amplification method, the mean-value theorem for integrals and Gamma function, explicit bounds for the unknown functions in the inequality is given clearly. The derived results can be applied in the study of fractional difference equations in Engineering.

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23

Luo, Danfeng, and Zhiguo Luo. "Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses." Filomat 33, no. 17 (2019): 5499–510. http://dx.doi.org/10.2298/fil1917499l.

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In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

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24

Wang, Wu Sheng, and Chun Miao Huang. "A Class of Singular Volterra-Fredholm Type Difference Inequality in Engineering." Applied Mechanics and Materials 571-572 (June 2014): 132–38. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.132.

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In this paper, we discuss a class of new weakly singular Volterra-Fredholm difference inequality, which is solved using change of variable, discrete Jensen inequality, Beta function, the mean-value theorem for integrals and amplification method, and explicit bounds for the unknown functions is given clearly. The derived results can be applied in the study of fractional difference equations in engineering.

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25

Wang, Wu Sheng, and Zong Yi Hou. "A Class of Volterra-Fredholm Difference Inequality with Weakly Singularity in Engineering." Applied Mechanics and Materials 571-572 (June 2014): 139–42. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.139.

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In this paper, we discuss a class of new Volterra-Fredholm weakly singular difference inequality. The explicit bounds for the unknown functions are given clearly by discrete Jensen inequality, Cauchy-Schwarz inequality, Gamma function, change of variable, the mean-value theorem for integrals and amplification method. The derived results can be applied in the study of fractional difference equations in engineering.

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26

Gohar, Abdelrahman, Mayada Younes, and Salah Doma. "Gohar Fractional Derivative: Theory and Applications." Journal of Fractional Calculus and Nonlinear Systems 4, no. 1 (2023): 17–34. http://dx.doi.org/10.48185/jfcns.v4i1.753.

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The local fractional derivatives marked the beginning of a new era in fractional calculus. Due to their that have never been observed before in the field, they are able to fill in the gaps left by the nonlocal fractional derivatives and substantially increase the field’s theoretical and applied potential. In this article, we introduce a new local fractional derivative that possesses some classical properties of the integer-order calculus, such as the product rule, the quotient rule, the linearity, and the chain rule. It meets the fractional extensions of Rolle’s theorem and the mean value theo

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27

Suwan, Iyad, Shahd Owies, Muayad Abussa, and Thabet Abdeljawad. "Monotonicity Analysis of Fractional Proportional Differences." Discrete Dynamics in Nature and Society 2020 (May 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/4867927.

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In this work, the nabla discrete new Riemann–Liouville and Caputo fractional proportional differences of order 0<ε<1 on the time scale ℤ are formulated. The differences and summations of discrete fractional proportional are detected on ℤ, and the fractional proportional sums associated to ∇cRχε,ρz with order 0<ε<1 are defined. The relation between nabla Riemann–Liouville and Caputo fractional proportional differences is derived. The monotonicity results for the nabla Caputo fractional proportional difference are proved; specifically, if ∇c−1Rχε,ρz>0 then χz is ερ −increasing, an

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28

KHAN, ZAREEN A., and HIJAZ AHMAD. "QUALITATIVE PROPERTIES OF SOLUTIONS OF FRACTIONAL DIFFERENTIAL AND DIFFERENCE EQUATIONS ARISING IN PHYSICAL MODELS." Fractals 29, no. 05 (2021): 2140024. http://dx.doi.org/10.1142/s0218348x21400247.

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Discrete fractional calculus (DFC) is suggested to interpret neural schemes with memory impacts. This study seeks to formulate some discrete fractional nonlinear inequalities with [Formula: see text] fractional sum operators that are used with some conventional and forthright inequalities. Taking into consideration, we recreate the explicit bounds of Gronwall-type inequalities by observing the principle of DFC for unknown functions here. Such inequalities are of new version relative to the current literature findings so far and can be used as a helpful method to evaluate the numerical solution

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29

Albadarneh, Ramzi B., Iqbal M. Batiha, Ahmad Adwai, Nedal Tahat, and A. K. Alomari. "Numerical approach of riemann-liouville fractional derivative operator." International Journal of Electrical and Computer Engineering (IJECE) 11, no. 6 (2021): 5367. http://dx.doi.org/10.11591/ijece.v11i6.pp5367-5378.

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<p>This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating the Riemann-Liouville fractional derivative operator. These formulas are derived by utilizing some of forthright computations, and by utilizing the so-called weighted mean value theorem (WMVT). Undoubtedly, such formulas will be extremely useful in establishing new approaches for several solutions of both linear and nonlinear fractionalorder differential equations. This assertion is confirmed by addressing several linear and n

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30

Ahmadian, Davood, and Omid Farkhondeh Rouz. "Boundedness and convergence analysis of stochastic differential equations with Hurst Brownian motion." Boletim da Sociedade Paranaense de Matemática 38, no. 5 (2019): 187–96. http://dx.doi.org/10.5269/bspm.v38i5.38313.

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In this paper, we discuss about the boundedness and convergence analysis of the fractional Brownian motion (FBM) with Hurst parameter H. By the simple analysis and using the mean value theorem for stochastic integrals we conclude that in case of decreasing diffusion function, the solution of FBM is bounded for any H ∈ (0,1). Also, we derive the convergence rate which shows efficiency and accuracy of the computed solutions.

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31

Albadarneh, Ramzi B., Iqbal Batiha, A. K. Alomari, and Nedal Tahat. "Numerical approach for approximating the Caputo fractional-order derivative operator." AIMS Mathematics 6, no. 11 (2021): 12743–56. http://dx.doi.org/10.3934/math.2021735.

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<abstract><p>This work aims to propose a new simple robust power series formula with its truncation error to approximate the Caputo fractional-order operator $ D_{a}^{\alpha}y(t) $ of order $ m-1 &lt; \alpha &lt; m $, where $ m\in\mathbb{N} $. The proposed formula, which are derived with the help of the weighted mean value theorem, is expressed ultimately in terms of a fractional-order series and its reminder term. This formula is used successfully to provide approximate solutions of linear and nonlinear fractional-order differential equations in the form of series solution

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32

Nazeer, Waqas, Ghulam Farid, Zabidin Salleh, and Ayesha Bibi. "On Opial-Type Inequalities for Superquadratic Functions and Applications in Fractional Calculus." Mathematical Problems in Engineering 2021 (June 29, 2021): 1–11. http://dx.doi.org/10.1155/2021/6379883.

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We have studied the Opial-type inequalities for superquadratic functions proved for arbitrary kernels. These are estimated by applying mean value theorems. Furthermore, by analyzing specific functions, the fractional integral and fractional derivative inequalities are obtained.

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33

Abd Alaal, Faisal E., Adel R. Hadhoud, Ayman A. Abdelaziz, and Taha Radwan. "On the Numerical Investigations of a Fractional-Order Mathematical Model for Middle East Respiratory Syndrome Outbreak." Fractal and Fractional 8, no. 9 (2024): 521. http://dx.doi.org/10.3390/fractalfract8090521.

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Middle East Respiratory Syndrome (MERS) is a human coronavirus subtype that poses a significant public health concern due to its ability to spread between individuals. This research aims to develop a fractional-order mathematical model to investigate the MERS pandemic and to subsequently develop two numerical methods to solve this model numerically to evaluate and comprehend the analysis results. The fixed-point theorem has been used to demonstrate the existence and uniqueness of the solution to the suggested model. We approximate the solutions of the proposed model using two numerical methods

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34

Liu, Shuanghua, Qin Qi, and Zhiming Hu. "An Improved Nonhomogeneous Grey Model with Fractional-Order Accumulation and Its Application." Journal of Mathematics 2021 (June 21, 2021): 1–11. http://dx.doi.org/10.1155/2021/9962565.

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The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particul

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35

Khan, Tahir, Zi-Shan Qian, Roman Ullah, et al. "The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model." Complexity 2021 (December 27, 2021): 1–18. http://dx.doi.org/10.1155/2021/8752161.

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We investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform

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36

IQBAL, SAJID, GHULAM FARID, JOSIP PEČARIĆ, and ARTION KASHURI. "Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators." Kragujevac Journal of Mathematics 45, no. 5 (2021): 797–813. http://dx.doi.org/10.46793/kgjmat2105.797i.

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In this paper we present variety of Hardy-type inequalities and their reﬁnements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modiﬁed extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

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37

Rajratana Maroti Kamble and Pramod Ramakant Kulkarni. "Extended fractional derivative: Some results involving classical properties and applications." Scientific Temper 15, no. 04 (2024): 3026–33. https://doi.org/10.58414/scientifictemper.2024.15.4.09.

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In this paper, considering the classical definition of derivative in the limit form, we can define a new fractional derivative called the extended fractional derivative, which depends upon two parameters α and a. For this new fractional derivative, we have proved the properties of classical derivatives such as the product rule, the quotient rule, the chain rule, Rolle’s and Lagrange’s mean value theorems, etc., which are nor satisfied by the existing fractional derivatives defined by Riemann Liouville, Caputo, Grunwald. Moreover, we have defined the extended fractional integral and proved some

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38

Abimbade, Sulaimon F., Furaha M. Chuma, Sunday O. Sangoniyi, Ramoshweu S. Lebelo, Kazeem O. Okosun, and Samson Olaniyi. "Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus." Mathematics 12, no. 10 (2024): 1593. http://dx.doi.org/10.3390/math12101593.

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In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynami

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39

Mohammed, Pshtiwan Othman, Thabet Abdeljawad, and Faraidun Kadir Hamasalh. "On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis." Mathematics 9, no. 11 (2021): 1303. http://dx.doi.org/10.3390/math9111303.

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Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-differenc

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40

Rehman, Atiq Ur, Ghulam Farid, and Yasir Mehboob. "Mean value Theorems associated to the differences of Opial-type inequalities and their fractional versions." Fractional Differential Calculus, no. 2 (2020): 213–24. http://dx.doi.org/10.7153/fdc-2020-10-13.

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41

Yang, Zhanying, and Jie Zhang. "Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays." Complexity 2019 (October 31, 2019): 1–22. http://dx.doi.org/10.1155/2019/2363707.

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This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions

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Khan, Tahir, Roman Ullah, Ali Yousef, Gul Zaman, Qasem M. Al-Mdallal, and Yasser Alraey. "Modeling and Dynamics of the Fractional Order SARS-CoV-2 Epidemiological Model." Complexity 2022 (September 27, 2022): 1–15. http://dx.doi.org/10.1155/2022/3846904.

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We propose a theoretical study to investigate the spread of the SARS-CoV-2 virus, reported in Wuhan, China. We develop a mathematical model based on the characteristic of the disease and then use fractional calculus to fractionalize it. We use the Caputo-Fabrizio operator for this purpose. We prove that the considered model has positive and bounded solutions. We calculate the threshold quantity of the proposed model and discuss its sensitivity analysis to find the role of every epidemic parameter and the relative impact on disease transmission. The threshold quantity (reproductive number) is u

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Bajjah, Bushra, and Mahmut Modanli. "Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator." Discrete Dynamics in Nature and Society 2024 (May 15, 2024): 1–26. http://dx.doi.org/10.1155/2024/2580745.

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In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number Rp°. The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the

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Khan, Tahir, Saeed Ahmad, Rahman Ullah, Ebenezer Bonyah, and Khursheed J. Ansari. "The asymptotic analysis of novel coronavirus disease via fractional-order epidemiological model." AIP Advances 12, no. 3 (2022): 035349. http://dx.doi.org/10.1063/5.0087253.

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We develop a model and investigate the temporal dynamics of the transmission of the novel coronavirus. The main sources of the coronavirus disease were bats and unknown hosts, which left the infection in the seafood market and became the major cause of the spread among the population. Evidence shows that the infection spiked due to the interaction between humans. Hence, the formulation of the model proposed in this study is based on human-to-human and reservoir-to-human interaction. We formulate the model by keeping in view the esthetic of the novel disease. We then fractionalize it with the a

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Pejovic, Branko, Vladan Micic, Mitar Perusic, Goran Tadic, Ljubica Vasiljevic, and Slavko Smiljanic. "Proposal for determining changes in entropy of semi ideal gas using mean values of temperature functions." Chemical Industry 68, no. 5 (2014): 615–28. http://dx.doi.org/10.2298/hemind130825090p.

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In a semi-ideal gas, entropy changes cannot be determined through the medium specific heat capacity in a manner as determined by the change of internal energy and enthalpy, i.e. the amount of heat exchanged. Taking this into account, the authors conducted two models through which it is possible to determine the change in the specific entropy of a semi-ideal gas for arbitrary temperature interval using the spread sheet method, using the mean values of the appropriate functions. The idea is to replace integration, which occurs here in evitably, with mean values of the previous functions. The mod

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Legrand, Alexandre, Emmanuelle Schneider, Pierre-Alain Gevenois, and André De Troyer. "Respiratory effects of the scalene and sternomastoid muscles in humans." Journal of Applied Physiology 94, no. 4 (2003): 1467–72. http://dx.doi.org/10.1152/japplphysiol.00869.2002.

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Previous studies have shown that in normal humans the change in airway opening pressure (ΔPao) produced by all the parasternal and external intercostal muscles during a maximal contraction is approximately −18 cmH2O. This value is substantially less negative than ΔPao values recorded during maximal static inspiratory efforts in subjects with complete diaphragmatic paralysis. In the present study, therefore, the respiratory effects of the two prominent inspiratory muscles of the neck, the sternomastoids and the scalenes, were evaluated by application of the Maxwell reciprocity theorem. Seven he

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Rebai, Hajer, Imen Abdennadher, and Ahmed Masmoudi. "Torque production improvement of a five phase fractional-slot PM machine under faulty operation." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 34, no. 6 (2015): 1758–70. http://dx.doi.org/10.1108/compel-06-2015-0240.

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Purpose – The purpose of this paper is to deal with several approach to recover the torque production capability of a five phase double-layer fractional-slot PM machine under faulty operation. The considered fault is an open-circuit coil in a given phase. Design/methodology/approach – In a first step, the mean futures, such as the phase back-EMFs and the electromagnetic torque, are computed by finite element analysis under healthy operation, and are taken as references. Then, they are investigated, under a faulty coil, for different approaches to recover the torque production capability. Findi

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Trokhimchuk, Yu Yu. "Mean-Value Theorem." Ukrainian Mathematical Journal 65, no. 9 (2014): 1418–25. http://dx.doi.org/10.1007/s11253-014-0869-z.

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Liu, Yuji. "A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications." Advances in Nonlinear Analysis 8, no. 1 (2017): 386–454. http://dx.doi.org/10.1515/anona-2016-0064.

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Abstract In this paper, we present a new method for converting boundary value problems of impulsive fractional differential equations to integral equations. Applications of this method are given to solve some types of anti-periodic boundary value problems for impulsive fractional differential equations. Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann–Liouville and Hadamard fractional derivatives with order {q\in(0,1)} , see Theorem 2, Theorem 4, Theorem 6 and Theorem 8

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Hilmi, Hozan, and Karwan H. F. Jwamer. "Existence and Uniqueness Solution of Fractional Order Regge Problem." JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences 30, no. 2 (2022): 80–96. http://dx.doi.org/10.29196/jubpas.v30i2.4186.

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In this paper, we look into a group of fractional boundary value problem equations involving fractional derivative fractional orders and there are two boundary value criteria in this equation. The existence and uniqueness solutions are obtained using the Banach fixed point theorem (Contraction mapping theorem) and the Schauder fixed point theorem. based on the method of fractional integral and integral operator, our primary findings are illustrated using examples.

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