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Journal articles on the topic 'Mean derivatives'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Bullen, P. S., and D. N. Sarkhel. "On Darboux and Mean Value Properties." Canadian Mathematical Bulletin 30, no. 2 (1987): 223–30. http://dx.doi.org/10.4153/cmb-1987-032-8.

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AbstractIn this paper we extend and greatly generalize, with some new information, the well known results that an approximately continuous function is Darboux, and that a finite approximate derivative has the mean value property and is Darboux. Our theorems on Darboux and mean value properties of derivatives include also those of selective derivatives and I-approximate derivatives.

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2

Pan, Xinyu. "Research on discrete differential solution methods for derivatives of chaotic systems." AIMS Mathematics 9, no. 12 (2024): 33995–4012. https://doi.org/10.3934/math.20241621.

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<p>The pivotal differential parameters inherent in chaotic systems hold paramount significance across diverse disciplines. This study delves into the distinctive features of discrete differential parameters within three typical chaotic systems: the logistic map, the henon map, and the tent map. A pivotal discovery emerges: both the mean value of the first-order continuous and discrete derivatives in the logistic map coincide, mirroring a similar behavior observed in the henon map. Leveraging the insights gained from the first derivative formulations, we introduce the discrete n-order der

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3

Zhou, Haiying, and Huainian Zhu. "Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference." Mathematics 12, no. 13 (2024): 2047. http://dx.doi.org/10.3390/math12132047.

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In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dep

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4

Glasserman, Paul. "Regenerative derivatives of regenerative sequences." Advances in Applied Probability 25, no. 1 (1993): 116–39. http://dx.doi.org/10.2307/1427499.

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Given a parametric family of regenerative processes on a common probability space, we investigate when the derivatives (with respect to the parameter) are regenerative. We primarily consider sequences satisfying explicit, Lipschitz recursions, such as the waiting times in many queueing systems, and show that derivatives regenerate together with the original sequence under reasonable monotonicity or continuity assumptions. The inputs to our recursions are i.i.d. or, more generally, governed by a Harris-ergodic Markov chain. For i.i.d. input we identify explicit regeneration points; otherwise, w

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5

Glasserman, Paul. "Regenerative derivatives of regenerative sequences." Advances in Applied Probability 25, no. 01 (1993): 116–39. http://dx.doi.org/10.1017/s0001867800025209.

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Given a parametric family of regenerative processes on a common probability space, we investigate when the derivatives (with respect to the parameter) are regenerative. We primarily consider sequences satisfying explicit, Lipschitz recursions, such as the waiting times in many queueing systems, and show that derivatives regenerate together with the original sequence under reasonable monotonicity or continuity assumptions. The inputs to our recursions are i.i.d. or, more generally, governed by a Harris-ergodic Markov chain. For i.i.d. input we identify explicit regeneration points; otherwise, w

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6

Mukhopadhyay, S. N., and S. Ray. "Mean value theorems for divided differences and approximate Peano derivatives." Mathematica Bohemica 134, no. 2 (2009): 165–71. http://dx.doi.org/10.21136/mb.2009.140651.

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7

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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8

Hari Pratap. "Memory Effect of Deformable Mean and Deformable Standard Deviation." Communications on Applied Nonlinear Analysis 32, no. 8s (2025): 439–43. https://doi.org/10.52783/cana.v32.3688.

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Memory effects can be easily understood with the help of fractional derivatives. In this paper with the help of Deformable fractional derivative we try to understand the role of deformability on memory effects of a normal distribution using moment generating function. First, we develop a formula for Deformable mean and Deformable standard deviation with the help of Deformable fractional derivative. Secondly, we calculate the value of Deformable mean and Deformable standard deviation for varying fractional order. Lastly, we draw plot of normal distribution for calculated value of Deformable mea

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9

Verma, Praneeta, and Anil Kumar. "STUDY ON MEAN VALUES OF AN ENTIRE FUNCTION AND ITS DERIVATIVES." jnanabha 54, no. 01 (2024): 180–84. http://dx.doi.org/10.58250/jnanabha.2024.54122.

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n this paper, we investigate mean values of an entire function and its derivative in the usual notation. It is obvious that generally λ1 ≤ λ and ρ1 ≤ ρ, Sugimura[12]there are entire Dirichlet’s series for which λ1 < λ and ρ1 < ρ. We have generally to distinguish between the limits as well as types of f(s) belonging to the same order ρ1 (0 < ρ1 < ∞) Bhan and Rastogi [1]We obtain some result of m2,k(σ) Kamthan [7]for the mean value of an entire Dirichlet’s series and its derivative. In this paper we shall establish some interesting results in term of theorems on mean values of an ent

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10

Andrade, Julio. "Mean values of derivatives of L-functions in function fields: III." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 04 (2018): 905–13. http://dx.doi.org/10.1017/prm.2018.53.

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AbstractIn this series of papers, we explore moments of derivatives of L-functions in function fields using classical analytic techniques such as character sums and approximate functional equation. The present paper is concerned with the study of mean values of derivatives of quadratic Dirichlet L-functions over function fields when the average is taken over monic and irreducible polynomials P in 𝔽q[T]. When the cardinality q of the ground field is fixed and the degree of P gets large, we obtain asymptotic formulas for the first moment of the first and the second derivative of this family of L

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11

Rajakumari, P. Evangelin Diana, and R. Gethsi Sharmila. "Runge-Kutta Method Based on the Linear Combination of Arithmetic Mean, Geometric Mean, and Centroidal Mean: A Numerical Solution for the Hybrid Fuzzy Differential Equation." Indian Journal Of Science And Technology 17, no. 18 (2024): 1860–67. http://dx.doi.org/10.17485/ijst/v17i18.75.

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Objectives: To find the absolute error of the Hybrid fuzzy differential equation with triangular fuzzy number since its membership function has a triangular form. Methods: The third order runge-kuttta method based on the linear combination of Arithmetic mean, Geometric mean and Centroidal mean is introduced to solve Hybrid fuzzy differential equation. Seikkala’s derivatives are considered, and Numerical example is given to demonstrate the effectiveness of the proposed method. Findings: The comparative study have been done between the proposed method and the existing third order runge-kutta met

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12

Rättyä, J. "n-th derivative characterisations, mean growth of derivatives and F(p, q, s)." Bulletin of the Australian Mathematical Society 68, no. 3 (2003): 405–21. http://dx.doi.org/10.1017/s0004972700037813.

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Various n-th derivative characterisations involving different kinds of oscillations of F(p,q,s) functions are established, and the mean growth of derivatives of F(p,q,s) functions is considered. Moreover, inclusion relations between certain analytic function spaces are discussed.

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13

Aczél, J. "A Mean Value Property of the Derivative of Quadratic Polynomials-without Mean Values and Derivatives." Mathematics Magazine 58, no. 1 (1985): 42. http://dx.doi.org/10.2307/2690237.

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14

Aczél, J. "A Mean Value Property of the Derivative of Quadratic Polynomials—without Mean Values and Derivatives." Mathematics Magazine 58, no. 1 (1985): 42–45. http://dx.doi.org/10.1080/0025570x.1985.11977147.

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15

FOUQUE, JEAN-PIERRE, GEORGE PAPANICOLAOU, and K. RONNIE SIRCAR. "MEAN-REVERTING STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 03, no. 01 (2000): 101–42. http://dx.doi.org/10.1142/s0219024900000061.

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We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tick-by-tick fluctuations of the index value, but it is fast mean-reverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis of the partial differential equation satisfied by derivative prices, utilizing the distinction be

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16

Kordyumov, G. D. "DERIVATIVES IN THE MEAN OF RANDOM PROCESSES AND DIFFUSION MODELS IN ECONOMICS." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 3 (2021): 26–30. http://dx.doi.org/10.14529/mmph210303.

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The article is devoted to diffusion models. The authors discuss the theoretical and methodological foundations of diffusion models in financial mathematics. Like the economic system, the modern world is developing rapidly. It seems impossible to predict what will happen tomorrow, how the emergence of new technologies will affect the market, and how changes in random factors will affect the product and the market as a whole. Diffusion models are one of the main methods for studying economic objects and processes. This is why it is so important to develop a diffusion model. The authors propose e

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17

Hosokawa, Satoshi, and Koichi Matsumoto. "Pricing interest rate derivatives with model risk." Journal of Financial Engineering 02, no. 01 (2015): 1550003. http://dx.doi.org/10.1142/s2345768615500038.

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This paper studies an interest rate derivative when there is the model risk in an interest rate model. We consider a mean reverting interest rate process whose volatility model is not known. Most of prices of interest rate derivatives cannot be determined uniquely, based on this interest rate model. We study the price bounds of a derivative and propose how to calculate the price bounds by a trinomial model. Further, we analyze the model risk of derivatives and their portfolios numerically.

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18

Akopyan, Arsenyi, and Herbert Edelsbrunner. "The Weighted Mean Curvature Derivative of a Space-Filling Diagram." Computational and Mathematical Biophysics 8, no. 1 (2020): 51–67. http://dx.doi.org/10.1515/cmb-2020-0100.

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AbstractRepresenting an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in

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19

Wojtyczka, Robert D., Andrzej Zięba, Arkadiusz Dziedzic, Małgorzata Kępa, and Danuta Idzik. "An Activity of Thioacyl Derivatives of 4-Aminoquinolinium Salts towards Biofilm Producing and Planktonic Forms of Coagulase-Negative Staphylococci." BioMed Research International 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/725939.

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Microorganisms present in different environments have developed specific mechanisms of settling on various abiotic and biotic surfaces by forming a biofilm. It seems to be well justified to search for new compounds enabling biofilm reduction, which is highly resistant to antibiotics. This study was thus an initial assessment of the antibacterial activity of two new quinoline derivatives of a structure of 3-thioacyl 1-methyl 4-arylaminoquinolinium salts against coagulase-negative staphylococci (CoNS) isolated from a hospital environment, in a form of both biofilms and in planktonic form. Thirty

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20

Martínez, Francisco, Inmaculada Martínez, Mohammed K. A. Kaabar, and Silvestre Paredes. "Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus." Journal of Mathematics 2021 (April 1, 2021): 1–7. http://dx.doi.org/10.1155/2021/5528537.

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The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable

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21

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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22

Zamzamir@Zamzamin, Zaminor, Razali Haron, Zatul Karamah Ahmad Baharul Ulum, and Anwar Hasan Abdullah Othman. "IMPACT OF DERIVATIVES USER ON FIRMS’ PERFORMANCE OF SHARI’AH COMPLIANT FIRMS." International Journal of Business and Society 24, no. 1 (2023): 1–17. http://dx.doi.org/10.33736/ijbs.5594.2023.

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The study examined the impact of derivatives usage on the performance of Shari'ah-compliant firms in Malaysia. The study employed a Generalised Method-of-Moment estimator (System-GMM) on a set of panel data from 2012 to 2017. A paired sample t-test for mean difference and a Wilcoxon Signed-ranks test was performed to examine the performance difference between users and non-users of derivatives. The study provided strong evidence of a significant difference in performance between users and non-users of derivatives. Moreover, the study observed better performance among derivative users than non-

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23

JORDAN, RICHARD, and CHARLES TIER. "ASYMPTOTIC APPROXIMATIONS FOR PRICING DERIVATIVES UNDER MEAN-REVERTING PROCESSES." International Journal of Theoretical and Applied Finance 19, no. 05 (2016): 1650030. http://dx.doi.org/10.1142/s0219024916500308.

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The problem of fast pricing, hedging, and calibrating of derivatives is considered when the underlying does not follow the standard Black–Scholes–Merton model but rather a mean-reverting and deterministic volatility model. Mean-reverting models are often used for volatility, commodities, and interest-rate derivatives, while the deterministic volatility accounts for the nonconstant implied volatility. Trading desks often use numerical methods for real-time pricing, hedging, and calibration when implementing such models. A more efficient alternative is to use an analytic formula, even if only ap

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24

Sasaki, Hiroaki, Yung-Kyun Noh, Gang Niu, and Masashi Sugiyama. "Direct Density Derivative Estimation." Neural Computation 28, no. 6 (2016): 1101–40. http://dx.doi.org/10.1162/neco_a_00835.

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Estimating the derivatives of probability density functions is an essential step in statistical data analysis. A naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives. However, this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator. To cope with this problem, in this letter, we propose a novel method that directly estimates density derivatives without going through density estimation. The proposed method provides computationally efficient estimation for the deriv

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25

O’Neill, Larry W., Tracy Haack, and Theodore Durland. "Estimation of Time-Averaged Surface Divergence and Vorticity from Satellite Ocean Vector Winds." Journal of Climate 28, no. 19 (2015): 7596–620. http://dx.doi.org/10.1175/jcli-d-15-0119.1.

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Abstract Two methods of computing the time-mean divergence and vorticity from satellite vector winds in rain-free (RF) and all-weather (AW) conditions are investigated. Consequences of removing rain-contaminated winds on the mean divergence and vorticity depend strongly on the order in which the time-average and spatial derivative operations are applied. Taking derivatives first and averages second (DFAS_RF) incorporates only those RF winds measured at the same time into the spatial derivatives. While preferable mathematically, this produces mean fields biased relative to their AW counterparts

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26

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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27

Akopyan, Arsenyi, and Herbert Edelsbrunner. "The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram." Computational and Mathematical Biophysics 8, no. 1 (2020): 74–88. http://dx.doi.org/10.1515/cmb-2020-0101.

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AbstractThe morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.

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28

Argyros, Ioannis K., and Manoj K. Singh. "On the Contraharmonic-mean Newton’s method(CHN)." Journal of Interdisciplinary Mathematics 26, no. 2 (2023): 231–43. http://dx.doi.org/10.47974/jim-1448.

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The objective of this study is to investigate the Contraharmonic-mean Newton’s method (CHN) for solving equations in Banach space. Local analysis has been performed by Taylor’s expansion utilizing high order derivatives and also using only the first derivatives appearing on the method. We have checked the theoretical results by comparing the CHN method with the Newton’s and related third order methods by Weerakoon et al. utilizing some test functions. The theoretical and numerical results are examined by the dynamical analysis of a selected test function.

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29

Ash, J. M., and R. L. Jones. "Mean value theorems for generalized Riemann derivatives." Proceedings of the American Mathematical Society 101, no. 2 (1987): 263. http://dx.doi.org/10.1090/s0002-9939-1987-0902539-2.

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30

Balázs, Katherine, and T. Kilgore. "Interpolation and simultaneous mean convergence of derivatives." Acta Mathematica Hungarica 61, no. 1-2 (1993): 63–72. http://dx.doi.org/10.1007/bf01872098.

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31

Mastroianni, Giuseppe, and Paul Nevai. "Mean convergence of derivatives of Lagrange interpolation." Journal of Computational and Applied Mathematics 34, no. 3 (1991): 385–96. http://dx.doi.org/10.1016/0377-0427(91)90096-3.

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32

Tenreiro Machado, J. A., Alexandra M. Galhano, Anabela M. Oliveira, and József K. Tar. "Approximating fractional derivatives through the generalized mean." Communications in Nonlinear Science and Numerical Simulation 14, no. 11 (2009): 3723–30. http://dx.doi.org/10.1016/j.cnsns.2009.03.004.

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Rafati, Pouria, Jalal Jafarzade, Akbar Hoseinnejad, Asieh Khalilpour, Mojtaba Taghizadeh Armaki, and Firoozeh Kermani. "Investigating the Effectiveness of Spirocyclopropane-Oxindole Derivatives on Clinical Isolates of Candida albicans." Hormozgan Medical Journal 28, no. 1 (2024): 41–48. http://dx.doi.org/10.34172/hmj.8325.

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Objectives: Given the spread of azole resistance in Candida albicans (C. albicans), searching for new potent compounds, such as spirocyclopropane-oxindole derivatives is important. This study evaluates the antifungal susceptibility of spirocyclopropane-oxindole derivatives on clinical isolates of C. albicans. Methods: Antifungal susceptibility of 50 clinical isolates of C. albicans to spirocyclopropane-oxindole derivatives (4a, 4b, and 4c), nystatin, and fluconazole were evaluated according to Clinical Laboratory Standards Institute (M27-S4) guidelines. The medicinal dilution range of the comp

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34

Gliklikh, Yu E. "Stochastic Equations and Inclusions with Mean Derivatives and Their Applications." Contemporary Mathematics. Fundamental Directions 68, no. 2 (2022): 191–337. http://dx.doi.org/10.22363/2413-3639-2022-68-2-191-337.

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This work is a detailed presentation of the results, mainly obtained in recent years by the author and his school of the research of mean derivatives of random processes, stochastic equations and inclusions with mean derivatives, as well as their applications in various mathematical disciplines, mainly in mathematical physics. In addition, the work contains introductory material on mean derivatives by E. Nelson, who introduced this concept in the 60s of the XXs century, the results of other researchers on this topic, and preliminary concepts from various areas of mathematics used in this work.

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Liu, Qing, Pingping Zhou, Pengjie Luo, and Pinggu Wu. "Occurrence of Furfural and Its Derivatives in Coffee Products in China and Estimation of Dietary Intake." Foods 12, no. 1 (2023): 200. http://dx.doi.org/10.3390/foods12010200.

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This is the first report on the content of furfural and its derivatives in coffee products in China. The concentrations of furfural and its derivatives in 449 sampled, commercially available coffee products in China were analyzed through a GC-MS technique, and the associated health risks were estimated. As a result, 5-hydroxymethyl furfural (5-HMF) was identified as the predominant derivative compound, with the highest concentration of 6035.0 mg/kg and detection frequency of 98.7%. The mean dietary exposures of 5-HMF, 5-MF(5-methylfurfural), and 2-F(2-furfural) in coffee products among Chinese

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36

S., Deb. "On Symmetric Riemann-Derivatives." Indian Journal of Advanced Mathematics (IJAM) 1, no. 2 (2021): 47–51. https://doi.org/10.54105/ijam.B1114.101221.

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The basic properties like monotoni city, Darboux property, mean value property of symmetric Riemann-derivatives of order n of a real valued function f at a point x of its domain (a closed interval) is studied. In some cases, function is considered to be continuous or semi-continuous.

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37

Xiulian, Wang, and Ning Jingrui. "Mean Convergence Rate of Derivatives by Lagrange Interpolation on Chebyshev Grids." Discrete Dynamics in Nature and Society 2011 (2011): 1–22. http://dx.doi.org/10.1155/2011/503561.

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We consider the rate of mean convergence of derivatives by Lagrange interpolation operators based on the Chebyshev nodes. Some estimates of error of the derivatives approximation in terms of the error of best approximation by polynomials are derived. Our results are sharp.

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38

Lipovetsky, Stan. "Specific Features of Polynomials in Several Examples." Axioms 13, no. 1 (2024): 43. http://dx.doi.org/10.3390/axioms13010043.

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This paper considers polynomial characteristics useful for a better understanding of the behaviour of these functions. Taylor series for the polynomials are described by the items with even and odd derivatives and powered changes in the argument, which leads to more specific studying of their properties. Connections between the derivative and antiderivative of the polynomial functions are defined. The structure of polynomial functions reveals their specific characteristic that the mean value of their roots equals the mean value of the locations of the critical points such as the extrema and in

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39

Xu, Dongpo, Cyrus Jahanchahi, Clive C. Took, and Danilo P. Mandic. "Enabling quaternion derivatives: the generalized HR calculus." Royal Society Open Science 2, no. 8 (2015): 150255. http://dx.doi.org/10.1098/rsos.150255.

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Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutati

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40

P, Evangelin Diana Rajakumari, and Gethsi Sharmila R. "Runge-Kutta Method Based on the Linear Combination of Arithmetic Mean, Geometric Mean, and Centroidal Mean: A Numerical Solution for the Hybrid Fuzzy Differential Equation." Indian Journal of Science and Technology 17, no. 18 (2024): 1860–67. https://doi.org/10.17485/IJST/v17i18.75.

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Abstract <strong>Objectives:</strong> To find the absolute error of the Hybrid fuzzy differential equation with triangular fuzzy number since its membership function has a triangular form. <strong>Methods:</strong> The third order runge-kuttta method based on the linear combination of Arithmetic mean, Geometric mean and Centroidal mean is introduced to solve Hybrid fuzzy differential equation. Seikkala’s derivatives are considered, and Numerical example is given to demonstrate the effectiveness of the proposed method. <strong>Findings:</strong> The comparative st

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41

Caputo, Michele. "Mean fractional-order-derivatives differential equations and filters." ANNALI DELL UNIVERSITA DI FERRARA 41, no. 1 (1995): 73–84. http://dx.doi.org/10.1007/bf02826009.

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42

Murty, M. Ram, and V. Kumar Murty. "Mean Values of Derivatives of Modular L-Series." Annals of Mathematics 133, no. 3 (1991): 447. http://dx.doi.org/10.2307/2944316.

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43

Motornyi, V. P. "On mean approximation of function and its derivatives." Dnipro University Mathematics Bulletin 26, no. 1 (2018): 56. http://dx.doi.org/10.15421/241807.

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Fejzić, H., C. Freiling, and D. Rinne. "A mean value theorem for generalized Riemann derivatives." Proceedings of the American Mathematical Society 136, no. 02 (2007): 569–76. http://dx.doi.org/10.1090/s0002-9939-07-08976-9.

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de Oliveira, Anselmo E., Roberto L. A. Haiduke, and Roy E. Bruns. "Atomic Mean Dipole Moment Derivatives and GAPT Charges." Journal of Physical Chemistry A 104, no. 22 (2000): 5320–27. http://dx.doi.org/10.1021/jp994405l.

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Criscuolo, G., B. Della Vecchia, and G. Mastroianni. "Hermite interpolation and mean convergence of its derivatives." Calcolo 28, no. 1-2 (1991): 111–27. http://dx.doi.org/10.1007/bf02575871.

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Bennett, Colin, and Manfred Stoll. "Derivatives of analytic functions and bounded mean oscillation." Archiv der Mathematik 47, no. 5 (1986): 438–42. http://dx.doi.org/10.1007/bf01189985.

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Huxley, M. N. "A mean value theorem for exponential sums." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 3 (1995): 304–7. http://dx.doi.org/10.1017/s1446788700037204.

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AbstractThe exponential sum S(x) = Σe(f(m + x)) has mean square size O(M), when m runs through M consecutive integers, f(x) satisfies bounds on the second and third derivatives, and x runs from 0 to 1.

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Glasserman, Paul, Jian-Qiang Hu, and Stephen G. Strickland. "Strongly Consistent Steady-State Derivative Estimates." Probability in the Engineering and Informational Sciences 5, no. 4 (1991): 391–413. http://dx.doi.org/10.1017/s0269964800002199.

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We establish strong consistency (i.e., almost sure convergence) of infinitesimal perturbation analysis (IPA) estimators of derivatives of steady-state means for a broad class of systems. Our results substantially extend previously available results on steady-state derivative estimation via IPA.Our basic assumption is that the process under study is regenerative, but our analysis uses regenerative structure in an indirect way: IPA estimators are typically biased over regenerative cycles, so straightforward differentiation of the regenerative ratio formula does not necessarily yield a valid esti

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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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