Log in

Relevant bibliographies by topics / Fractional calculus / Journal articles

To see the other types of publications on this topic, follow the link: Fractional calculus.

Journal articles on the topic 'Fractional calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Fractional calculus.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Feng, Xiaobing, and Mitchell Sutton. "A new theory of fractional differential calculus." Analysis and Applications 19, no. 04 (2021): 715–50. http://dx.doi.org/10.1142/s0219530521500019.

Full text

Abstract:

This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize what functions are fractionally differentiable. Various calculus rules including a fundamental theorem calculus, product and chain rules, and integration by parts formulas are established for weak fractional derivatives. Additionally, relationsh

APA, Harvard, Vancouver, ISO, and other styles

2

Baleanu, Dumitru. "About Fractional Calculus of Singular Lagrangians." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 4 (2005): 395–98. http://dx.doi.org/10.20965/jaciii.2005.p0395.

Full text

Abstract:

In this paper the solutions of the fractional Euler-Lagrange quations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.

APA, Harvard, Vancouver, ISO, and other styles

3

Zhao, Yan Chun. "Design and Application of Digital Filter Based on Calculus Computing Concept." Applied Mechanics and Materials 513-517 (February 2014): 3151–55. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.3151.

Full text

Abstract:

Calculus has been widely applied in engineering fields. The development of Integer order calculus theory is more mature in the project which can obtain fractional calculus theory through the promotion of integration order. It extends the flexibility of calculation and achieves the engineering analysis of multi-degree of freedom. According to fractional calculus features and the characteristics of fractional calculus, this paper treats the frequency domain as the object of study and gives the fractional calculus definition of the frequency characteristics. It also designs the mathematical model

APA, Harvard, Vancouver, ISO, and other styles

4

Chii-Huei, Yu. "Using Integration by Parts for Fractional Calculus to Solve Some Fractional Integral Problems." International Journal of Electrical and Electronics Research 11, no. 2 (2023): 1–5. https://doi.org/10.5281/zenodo.7830903.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we solve some fractional integrals by using integration by parts for fractional calculus. A new multiplication of fractional analytic functions plays an important role in this article. In fact, our results are generalizations of traditional calculus results. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, fractional integrals, integration by parts for fractional calculus, new multiplication, fractional analytic functions. <strong>Title:</strong> Using Integration

APA, Harvard, Vancouver, ISO, and other styles

5

Chii-Huei, Yu. "An Improper Fractional Integral Involving Fractional Exponential Function." International Journal of Recent Research in Mathematics Computer Science and Information Technology 10, no. 1 (2023): 57–61. https://doi.org/10.5281/zenodo.8248860.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we use integration by parts for fractional calculus to solve an improper fractional integral involving fractional exponential function. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, integration by parts for fractional calculus, improper fractional integral, fractional exponential functi

APA, Harvard, Vancouver, ISO, and other styles

6

Chii-Huei, Yu. "A Study of Two Fractional Integral Problems Based on Jumarie Type of Riemann-Liouville Fractional Calculus." International Journal of Civil and Structural Engineering Research 12, no. 2 (2024): 15–19. https://doi.org/10.5281/zenodo.13982262.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we find the exact solutions of two fractional integrals. Integration by parts for fractional calculus and a new multiplication of fractional analytic functions play important roles in this article. In fact, our results are generalizations of classical calculus results.  <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, fractional integrals, integration by parts for fractional calculus, new multiplication, fractional analytic functions. <strong>Title:</strong> A

APA, Harvard, Vancouver, ISO, and other styles

7

Chii-Huei, Yu, and Yang Kuang-Wu. "Solving Some Type of Improper Fractional Integral Using Differentiation under Fractional Integral Sign and Integration by Parts for Fractional Calculus." International Journal of Engineering Research and Reviews 12, no. 4 (2024): 34–38. https://doi.org/10.5281/zenodo.13939320.

Full text

Abstract:

<strong>Abstract: </strong>In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study some type of improper fractional integral. We can obtain the exact solution of this improper fractional integral by using differentiation under fractional integral sign and integration by parts for fractional calculus. In fact, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, new multiplication, fractional analytic functi

APA, Harvard, Vancouver, ISO, and other styles

8

Sabzikar, Farzad, Mark M. Meerschaert, and Jinghua Chen. "Tempered fractional calculus." Journal of Computational Physics 293 (July 2015): 14–28. http://dx.doi.org/10.1016/j.jcp.2014.04.024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Lubich, Ch. "Discretized Fractional Calculus." SIAM Journal on Mathematical Analysis 17, no. 3 (1986): 704–19. http://dx.doi.org/10.1137/0517050.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Tarasov, Vasily E. "Lattice fractional calculus." Applied Mathematics and Computation 257 (April 2015): 12–33. http://dx.doi.org/10.1016/j.amc.2014.11.033.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Cont, Rama, and Ruhong Jin. "Fractional Ito calculus." Transactions of the American Mathematical Society, Series B 11, no. 22 (2024): 727–61. http://dx.doi.org/10.1090/btran/185.

Full text

Abstract:

We derive Itô–type change of variable formulas for smooth functionals of irregular paths with nonzero p p th variation along a sequence of partitions, where p ≥ 1 p \geq 1 is arbitrary, in terms of fractional derivative operators. Our results extend the results of the Föllmer–Itô calculus to the general case of paths with ‘fractional’ regularity. In the case where p p is not an integer, we show that the change of variable formula may sometimes contain a nonzero ‘fractional’ Itô remainder term and provide a representation for this remainder term. These results are then extended to functionals o

APA, Harvard, Vancouver, ISO, and other styles

12

Chii-Huei, Yu. "Methods for Solving Some Fractional Integral." International Journal of Electrical and Electronics Research 11, no. 1 (2023): 1–5. https://doi.org/10.5281/zenodo.7515836.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we evaluate some fractional integral. The main methods we used are fractional L’Hospital’s rule, integration by parts for fractional calculus, and a new multiplication of fractional analytic functions. In fact, our result is the generalization of classical calculus result. <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, fractional integral, fractional L’Hospital’s rule, integration by parts for fractional calculus, new mul

APA, Harvard, Vancouver, ISO, and other styles

13

Hanif, Usama, Ammara Nosheen, Rabia Bibi, Khuram Ali Khan, and Hamid Reza Moradi. "Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals." Mathematical Problems in Engineering 2021 (May 28, 2021): 1–14. http://dx.doi.org/10.1155/2021/9939468.

Full text

Abstract:

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

APA, Harvard, Vancouver, ISO, and other styles

14

Chii-Huei, Yu. "Application of Integration by Parts for Fractional Calculus in Solving Two Types of Fractional Definite Integrals." International Journal of Novel Research in Electrical and Mechanical Engineering 10, no. 1 (2023): 79–84. https://doi.org/10.5281/zenodo.8033205.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we solve two types of fractional definite integrals of fractional trigonometric functions. The exact solutions of these two types of fractional definite integrals can be obtained by using integration by parts for fractional calculus. Moreover, we give some examples to illustrate our results. On the other hand, our results are generalizations of the classical calculus results.     <strong>Keywords:</strong>

APA, Harvard, Vancouver, ISO, and other styles

15

Chii-Huei, Yu. "A New Definition of Fractional Calculus." International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE) 10, no. 3 (2023): 5–9. https://doi.org/10.5281/zenodo.8314984.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on a new multiplication of fractional analytic functions, we define a new fractional calculus. Moreover, we provide some properties of this new fractional calculus. In fact, our results are generalizations of classical calculus results. <strong>Keywords:</strong> New multiplication, fractional analytic functions, new fractional calculus. <strong>Title:</strong> A New Definition of Fractional Calculus <strong>Author:</strong> Chii-Huei Yu <strong>International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)</strong>

APA, Harvard, Vancouver, ISO, and other styles

16

Chii-Huei, Yu. "Evaluating an Improper Fractional Integral Based on Jumarie's Modified Riemann-Liouville Fractional Calculus." International Journal of Computer Science and Information Technology Research 11, no. 1 (2023): 22–27. https://doi.org/10.5281/zenodo.7551811.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral.  Change of variable for fractional calculus, integration by parts for fractional calculus, fractional L’Hospital’s rule, and a new multiplication of fractional analytic functions play important roles in this article. In fact, our result is a generalization of the traditional calculus result. <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, improper fractional integ

APA, Harvard, Vancouver, ISO, and other styles

17

Zine, Houssine, and Delfim F. M. Torres. "A Stochastic Fractional Calculus with Applications to Variational Principles." Fractal and Fractional 4, no. 3 (2020): 38. http://dx.doi.org/10.3390/fractalfract4030038.

Full text

Abstract:

We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler–Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.

APA, Harvard, Vancouver, ISO, and other styles

18

Tarasov, Vasily E. "General Fractional Calculus in Multi-Dimensional Space: Riesz Form." Mathematics 11, no. 7 (2023): 1651. http://dx.doi.org/10.3390/math11071651.

Full text

Abstract:

An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949. The proposed Riesz form of GFC can be considered as an extension GFC from the positive real line and the Laplace convolution to the m-dimensional Euclidean space and the Fourier convolution. To formulate the general fractional calculus in the Riesz form, the Luchko approach to construction of the GFC, which was suggested by Yuri Luchko in 2021, is used. The general fractional integrals and derivatives are defined as convolution-typ

APA, Harvard, Vancouver, ISO, and other styles

19

Sabatier, Jocelyn. "Design of Fractional Calculus Free Controllers with Fractional Behaviors." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18 (December 31, 2023): 602–11. http://dx.doi.org/10.37394/23203.2023.18.62.

Full text

Abstract:

Faced with the complexity and drawbacks of fractional calculus highlighted in the literature, this paper proposes simple solutions to avoid its use in the field of feedback control and especially to define fractional PID- and CRONE-like controllers. It shows that it is possible to generate fractional behaviors, which are known since the work of Bode to be useful in the field of control, without invoking fractional calculus and fractional models. Fractional calculus based models and fractional behaviors are indeed two different concepts: one denotes a particular class of models and the other a

APA, Harvard, Vancouver, ISO, and other styles

20

Tarasov, Vasily E. "General Fractional Vector Calculus." Mathematics 9, no. 21 (2021): 2816. http://dx.doi.org/10.3390/math9212816.

Full text

Abstract:

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency involves proving generalizations of all fundamental theorems of vector calculus for generalized kernels of operators. In the generalization of FVC from power-law nonlocality to the general form of nonlocality in space, we use the general fractional calculus (GFC) in the Luchko approach, which was published in 2021. This paper proposed the following: (I)

APA, Harvard, Vancouver, ISO, and other styles

21

Mishura, Yuliya, Olha Hopkalo, and Hanna Zhelezniak. "Elements of fractional calculus. Fractional integrals." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2022): 11–19. http://dx.doi.org/10.17721/1812-5409.2022/1.1.

Full text

Abstract:

The paper is devoted to the basic properties of fractional integrals. It is a survey of the well-known properties of fractional integrals, however, the authors tried to present the known information about fractional integrals as short and transparently as possible. We introduce fractional integrals on the compact interval and on the semi-axes, consider the famous Hardy-Littlewood theorem and other properties of integrability of fractional integrals. Among other basic properties, we consider Holder continuity and establish to what extent fractional integration increases the smoothness of the in

APA, Harvard, Vancouver, ISO, and other styles

22

Medina, Gustavo D., Nelson R. Ojeda, Jose H. Pereira, and Luis G. Romero. "Fractional Laplace transform and fractional calculus." International Mathematical Forum 12, no. 20 (2017): 991–1000. http://dx.doi.org/10.12988/imf.2017.71194.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Peng, Gang, Zhanqing Chen, and Jiarui Chen. "Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method." Advances in Civil Engineering 2018 (September 26, 2018): 1–6. http://dx.doi.org/10.1155/2018/1472840.

Full text

Abstract:

The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the

APA, Harvard, Vancouver, ISO, and other styles

24

Chii-Huei, Yu. "A Fractional Integral Involving Fractional Trigonometric Function." International Journal of Recent Research in Interdisciplinary Sciences (IJRRIS) 10, no. 3 (2023): 21–24. https://doi.org/10.5281/zenodo.8176924.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study a fractional integral involving fractional trigonometric function. In fact, our result is a generalization of traditional calculus result. <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, fractional integral, fractional trigonometric function. <strong>Title:</strong> A Fractional Integral Involving Fractional Trigonometric Function <strong>Author:</

APA, Harvard, Vancouver, ISO, and other styles

25

Chii-Huei, Yu. "Evaluating the Fractional Integrals of Some Fractional Rational Functions." International Journal of Mathematics and Physical Sciences Research 10, no. 1 (2022): 14–18. https://doi.org/10.5281/zenodo.6572879.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, the fractional integration problem of fractional rational functions is studied based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions. The main methods we used are the chain rule for fractional derivatives and the partial fraction method. On the other hand, we give some examples to illustrate how to calculate fractional integrals of some fractional rational functions. In fact, these results are extensions of the results in traditional calculus. <strong>Keywords:</strong> F

APA, Harvard, Vancouver, ISO, and other styles

26

Gohar, Abdelrahman, Mayada Younes, and Salah Doma. "On Gohar Fractional Calculus." Journal of Fractional Calculus and Nonlinear Systems 5, no. 1 (2024): 32–51. http://dx.doi.org/10.48185/jfcns.v5i1.1048.

Full text

Abstract:

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional

APA, Harvard, Vancouver, ISO, and other styles

27

Huang, Guo, Hong-ying Qin, Qingli Chen, Zhanzhan Shi, Shan Jiang, and Chenying Huang. "Research on Application of Fractional Calculus Operator in Image Underlying Processing." Fractal and Fractional 8, no. 1 (2024): 37. http://dx.doi.org/10.3390/fractalfract8010037.

Full text

Abstract:

Fractional calculus extends traditional, integer-based calculus to include non-integer orders, offering a powerful tool for a range of engineering applications, including image processing. This work delves into the utility of fractional calculus in two crucial aspects of image processing: image enhancement and denoising. We explore the foundational theories of fractional calculus together with its amplitude–frequency characteristics. Our focus is on the effectiveness of fractional differential operators in enhancing image features and reducing noise. Experimental results reveal that fractional

APA, Harvard, Vancouver, ISO, and other styles

28

Savita, Sharma. "New Advancements in the Applications of Fractional Calculus in Science and Engineering." International Journal of Trend in Scientific Research and Development 1, no. 6 (2017): 471–76. https://doi.org/10.31142/ijtsrd3579.

Full text

Abstract:

Fractional Calculus is a study of an extension of derivatives and integrals to non integer orders and also linking its origins with classical integral and di erential calculus. The interesting part of this subject is that fractional derivatives and integrals are not a local or point property or quantity. In some few years considerable interest in fractional calculus has been seen by the applications it finds in various areas of engineering, science, applied mathematics, finance and bio engineering as possibly it includes fractal phenomena too. This paper deals with the researchers of engineeri

APA, Harvard, Vancouver, ISO, and other styles

29

Chii-Huei, Yu. "Techniques for Solving Some Fractional Integrals." International Journal of Recent Research in Interdisciplinary Sciences 9, no. 2 (2022): 53–59. https://doi.org/10.5281/zenodo.6598936.

Full text

Abstract:

<strong>Abstract:</strong> This paper studies some fractional integrals based on Jumarie type of Riemann Liouville (R-L) fractional calculus. The main method used in this article is the change of variables for fractional calculus. A new multiplication of fractional analytic functions plays an important role in this paper. We give some examples to illustrate how to evaluate the fractional integrals. And these results we obtained are natural generalizations of the results in classical calculus. <strong>Keywords:</strong> Fractional integrals, Jumarie type of R-L fractional calculus, change of va

APA, Harvard, Vancouver, ISO, and other styles

30

Chii-Huei, Yu. "Research on a Fractional Integral of Fractional Rational Function." International Journal of Recent Research in Mathematics Computer Science and Information Technology 10, no. 1 (2023): 42–45. https://doi.org/10.5281/zenodo.8168839.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, a fractional integral of fractional rational is studied. In addition, our result is a generalization of classical calculus result. <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, new multiplication, fractional analytic functions, fractional integral, fractional rational function. <strong>Title:</strong> Research on a Fractional Integral of Fractional Rational Function <strong>Author:</stro

APA, Harvard, Vancouver, ISO, and other styles

31

Liu, Zelin, Xiaobin Yu, and Yajun Yin. "On the Rigorous Correspondence Between Operator Fractional Powers and Fractional Derivatives via the Sonine Kernel." Fractal and Fractional 8, no. 11 (2024): 653. http://dx.doi.org/10.3390/fractalfract8110653.

Full text

Abstract:

Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address these challenges, we have developed a universal framework for defining the fractional calculus operators using the generalized fractional calculus with the Sonine kernel. In this framework, we prove that the α-th power of a differential operator corresponds precisely to the α-th fractional derivative, ensuring both accuracy and consistency. Th

APA, Harvard, Vancouver, ISO, and other styles

32

Chii-Huei, Yu. "Two Fractional Integrals Involving Fractional Tangent Function." International Journal of Novel Research in Engineering and Science 10, no. 1 (2023): 7–12. https://doi.org/10.5281/zenodo.8047031.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study two fractional integrals involving fractional tangent function. We can obtain the exact solutions of these two fractional integrals by using some techniques. Moreover, our results are generalizations of the results of ordinary calculus.     <strong>Keywords:</strong> Jumarie type of R-L fractional calculus, new multiplication, fractional analytic functions, fractional integrals, fractional tangent

APA, Harvard, Vancouver, ISO, and other styles

33

Raja, Valarmathi, and Arulprakash Gowrisankar. "On the Variable Order Fractional Calculus Characterization for the Hidden Variable Fractal Interpolation Function." Fractal and Fractional 7, no. 1 (2022): 34. http://dx.doi.org/10.3390/fractalfract7010034.

Full text

Abstract:

In this study, the variable order fractional calculus of the hidden variable fractal interpolation function is explored. It extends the constant order fractional calculus to the case of variable order. The Riemann–Liouville and the Weyl–Marchaud variable order fractional calculus are investigated for hidden variable fractal interpolation function. Moreover, the conditions for the variable fractional order μ on a specified range are also derived. It is observed that, under certain conditions, the Riemann–Liouville and the Weyl–Marchaud variable order fractional calculus of the hidden variable f

APA, Harvard, Vancouver, ISO, and other styles

34

S., V. Nakade, and N. Ingle R. "Note on Integral Transform of Fractional Calculus." International Journal of Research and Review 6, no. 2 (2019): 106–10. https://doi.org/10.5281/zenodo.3987092.

Full text

Abstract:

In recent years Fractional Calculus is highly growing field in research because of its wide applicability and interdisciplinary approach. In this article we study various integral transform particularly Laplace Transform, Mellin Transform, of Fractional calculus i.e. Fractional derivative and Fractional Integral particularly of Riemann-Liouville Fractional derivative, Riemann-Liouville Fractional integral, Caputo’s Fractional derivative and their properties.

APA, Harvard, Vancouver, ISO, and other styles

35

Failla, Giuseppe, and Massimiliano Zingales. "Advanced materials modelling via fractional calculus: challenges and perspectives." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20200050. http://dx.doi.org/10.1098/rsta.2020.0050.

Full text

Abstract:

Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The t

APA, Harvard, Vancouver, ISO, and other styles

36

Gulsen, Tuba, Sertac Goktas, Thabet Abdeljawad, and Yusuf Gurefe. "Sturm-Liouville problem in multiplicative fractional calculus." AIMS Mathematics 9, no. 8 (2024): 22794–812. http://dx.doi.org/10.3934/math.20241109.

Full text

Abstract:

<p>Multiplicative calculus, or geometric calculus, is an alternative to classical calculus that relies on division and multiplication as opposed to addition and subtraction, which are the basic operations of classical calculus. It offers a geometric interpretation that is especially helpful for simulating systems that degrade or expand exponentially. Multiplicative calculus may be extended to fractional orders, much as classical calculus, which enables the analysis of systems having fractional scaling properties. So, in this paper, the well-known Sturm-Liouville problem in fractional cal

APA, Harvard, Vancouver, ISO, and other styles

37

Lazorenko, O., and L. Chernogor. "FRACTAL RADIOPHYSICS. PART 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS." Radio physics and radio astronomy 29, no. 1 (2024): 046–67. http://dx.doi.org/10.15407/rpra29.01.046.

Full text

Abstract:

Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics. The present work is an overview of the principal theoretical and practical ideas concerning "fractalization" in radio physics. The purpose is a systematic presentation of the main practical results suitable for application of the fractional calculus in modern theoretical radiophysics. Methods and Methodology. The basic theoretical principles of fractional calculus are outlined in a structured form. Results of applying fractional calculus metho

APA, Harvard, Vancouver, ISO, and other styles

38

David, S. A., J. L. Linares, and E. M. J. A. Pallone. "Fractional order calculus: historical apologia, basic concepts and some applications." Revista Brasileira de Ensino de Física 33, no. 4 (2011): 4302. http://dx.doi.org/10.1590/s1806-11172011000400002.

Full text

Abstract:

Fractional order calculus (FOC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. However, until recently, it has been investigated mainly from a mathematical point of view. Advances in the field of fractals have revealed its subtle relationships with fractional calculus. Nonetheless, fractional calculus is generally excluded from standard courses in mathematics, partly because many mathematicians are unfamiliar with its nature and its applications. This area has emerged as a useful tool among

APA, Harvard, Vancouver, ISO, and other styles

39

Wei, Yiheng, Linlin Zhao, Xuan Zhao, and Jinde Cao. "Enhancing the Mathematical Theory of Nabla Tempered Fractional Calculus: Several Useful Equations." Fractal and Fractional 7, no. 4 (2023): 330. http://dx.doi.org/10.3390/fractalfract7040330.

Full text

Abstract:

Although many applications of fractional calculus have been reported in literature, modeling the physical world using this technique is still a challenge. One of the main difficulties in solving this problem is that the long memory property is necessary, whereas the infinite memory is undesirable. To address this challenge, a new type of nabla fractional calculus with a weight function is formulated, which combines the benefits of nabla fractional calculus and its tempered counterpart, making it highly valuable for modeling practical systems. However, many properties of this calculus are still

APA, Harvard, Vancouver, ISO, and other styles

40

Sikora, Ryszard, and Stanislaw Pawłowski. "Fractional derivatives and the laws of electrical engineering." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4 (2018): 1384–91. http://dx.doi.org/10.1108/compel-08-2017-0347.

Full text

Abstract:

Purpose This paper aims to evaluate the possibilities of fractional calculus application in electrical circuits and magnetic field theories. Design/methodology/approach The analysis of mathematical notation is used for physical phenomena description. The analysis aims to challenge or prove the correctness of applied notation. Findings Fractional calculus is sometimes applied correctly and sometimes erroneously in electrical engineering. Originality/value This paper provides guidelines regarding correct application of fractional calculus in description of electrical circuits’ phenomena. It can

APA, Harvard, Vancouver, ISO, and other styles

41

Rani, Noosheza, and Arran Fernandez. "An operational calculus formulation of fractional calculus with general analytic kernels." Electronic Research Archive 30, no. 12 (2022): 4238–55. http://dx.doi.org/10.3934/era.2022216.

Full text

Abstract:

<abstract><p>Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series. We interpret these operators from an algebraic viewpoint, using Mikusiński's operational calculus, and utilise this algebraic formalism to solve some fractional differential equations.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

42

Chii-Huei, Yu. "Methods for Solving Some Type of Improper Fractional Integral." International Journal of Engineering Research and Reviews 11, no. 2 (2023): 14–18. https://doi.org/10.5281/zenodo.7886143.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, we use differentiation under fractional integral sign and integration by parts for fractional calculus to find the exact solution of some type of improper fractional integral. Jumarie type of Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions play important roles in this paper. On the other hand, some examples are provided to illustrate our result. In fact, our result is a generalization of ordinary calculus result. <strong>Keywords:</strong>  Differentiation under fractional integral sign, integr

APA, Harvard, Vancouver, ISO, and other styles

43

Chii-Huei, Yu. "Fractional Integral Problems of Some Fractional Trigonometric Functions." International Journal of Novel Research in Electrical and Mechanical Engineering 10, no. 1 (2023): 74–78. https://doi.org/10.5281/zenodo.7962202.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study the fractional integral problems of fractional trigonometric functions. The solutions of the fractional integrals can be obtained by using some techniques. In addition, we give some examples to illustrate our results. On the other hand, our results are generalizations of the traditional calculus results.     <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, new m

APA, Harvard, Vancouver, ISO, and other styles

44

Bas, Erdal, Resat Yilmazer, and Etibar Panakhov. "Fractional Solutions of Bessel Equation with -Method." Scientific World Journal 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/685695.

Full text

Abstract:

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the -fractional calculus operator method, we derive the fractional solutions of the equation.

APA, Harvard, Vancouver, ISO, and other styles

45

Chii-Huei, Yu. "Research on Fractional Integral Problems of Two Fractional Rational Functions." International Journal of Novel Research in Interdisciplinary Studies 10, no. 3 (2023): 11–17. https://doi.org/10.5281/zenodo.8009760.

Full text

Abstract:

<strong>Abstract:</strong> In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus and a new multiplication of fractional analytic functions, we study fractional integral problems of two fractional rational functions. Using some methods, the exact solutions of these two fractional integrals can be obtained. Moreover, our results are generalizations of classical calculus results.     <strong>Keywords:</strong> Jumarie’s modified R-L fractional calculus, new multiplication, fractional analytic functions, fractional integral, fraction

APA, Harvard, Vancouver, ISO, and other styles

46

Magin, Richard, Xu Feng, and Dumitru Baleanu. "Fractional Calculus in NMR." IFAC Proceedings Volumes 41, no. 2 (2008): 9613–18. http://dx.doi.org/10.3182/20080706-5-kr-1001.01626.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Anastassiou, George A. "Fuzzy fractional calculus revisited." New Trends in Mathematical Science 1 Proceeding, no. 9 (2021): 173–90. http://dx.doi.org/10.20852/ntmsci.2021.447.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

MA, LI, and CHANGPIN LI. "ON HADAMARD FRACTIONAL CALCULUS." Fractals 25, no. 03 (2017): 1750033. http://dx.doi.org/10.1142/s0218348x17500335.

Full text

Abstract:

This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the Hadamard-type fractional operators. Then, the definite conditions of certain class of Hadamard-type fractional differential equations (HTFDEs) are proposed through the Banach contraction mapping principle. Finally, we prove a novel Gronwall inequality with weak singularity and analyze the dependence of solutions of HTFDEs on the derivative order and the perturbation terms along with the proposed initial value conditions. The illustrativ

APA, Harvard, Vancouver, ISO, and other styles

49

Banerji, P. K., and Deshna Loonker. "Marvels of fractional calculus." Tbilisi Mathematical Journal 10, no. 1 (2017): 295–314. http://dx.doi.org/10.1515/tmj-2017-0019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Eloe, Paul, and Jeffrey Neugebauer. "Concavity in fractional calculus." Filomat 32, no. 9 (2018): 3123–28. http://dx.doi.org/10.2298/fil1809123e.

Full text

Abstract:

We discuss a concavity like property for functions u satisfying D?0+u ? C[0, b] with u(0) = 0 and -D?0+u(t) ? 0 for all t ? [0,b]. We develop the property for ? ? (1,2], where D?0+ is the standard Riemann-Liouville fractional derivative. We observe the property is also valid in the case ? = 1. Finally, we show that under certain conditions, -D?0+u(t) ? 0 implies u is concave in the classical sense.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!