Articles de revues : « Fractional differentiation »

1

Anastassiou, George A. "Multiparameter Fractional Differentiation with non singular kernel." Issues of Analysis 28, no. 3 (2021): 15–30. http://dx.doi.org/10.15393/j3.art.2021.10810.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

2

Gladkov, S. O., and S. B. Bogdanova. "ON FRACTIONAL DIFFERENTIATION." Vestnik of Samara University. Natural Science Series 24, no. 3 (2018): 7. http://dx.doi.org/10.18287/2541-7525-2018-24-3-7-13.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

3

TARASOV, VASILY E. "REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS." International Journal of Modern Physics B 27, no. 09 (2013): 1330005. http://dx.doi.org/10.1142/s0217979213300053.

Texte intégral

Résumé :

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods in the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of noninteger order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.

Styles APA, Harvard, Vancouver, ISO, etc.

4

Khalil, Anfal, and Basim Albuohimad. "Fractional Integration and Differentiation by new Transformation." Wasit Journal for Pure sciences 2, no. 2 (2023): 51–60. http://dx.doi.org/10.31185/wjps.107.

Texte intégral

Résumé :

In opposite to differentiation and integration of integer order, an important type of differentiation and integration is the so - called “ Fractional Calculus (FC) ” in which the differentiation and integration is of non-integer order. The idea of this work is to use a new transformation known as the Extension AL-Zughair Transform (EZT) for fractional calculus, so we reviewed some basic properties and definitions of (FC) such as differentiation and integration with Riemann-Liouvial operator. We reinforced this transformation for fractional differentiation and integration with some application examples at the end of the article for simplicity the Fractional Integrals and Fractional Derivatives

Styles APA, Harvard, Vancouver, ISO, etc.

5

Chii-Huei, Yu. "Application of Differentiation under Fractional Integral Sign." International Journal of Mathematics and Physical Sciences Research 10, no. 2 (2022): 40–46. https://doi.org/10.5281/zenodo.7486538.

Texte intégral

Résumé :

Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we use differentiation under fractional integral sign to evaluate two improper 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 the results in ordinary calculus. Keywords: Jumarie type of R-L fractional calculus, differentiation under fractional integral sign, improper fractional integrals, integration by parts, new multiplication, fractional analytic functions. Title: Application of Differentiation under Fractional Integral Sign Author: Chii-Huei Yu International Journal of Mathematics and Physical Sciences Research   ISSN 2348-5736 (Online) Vol. 10, Issue 2, October 2022 - March 2023 Page No: 40-46 Research Publish Journals Website: www.researchpublish.com Published Date: 27-December-2022 DOI: https://doi.org/10.5281/zenodo.7486538 Paper Download Link (Source) https://www.researchpublish.com/papers/application-of-differentiation-under-fractional-integral-sign

Styles APA, Harvard, Vancouver, ISO, etc.

6

Petrosyan, Garik G. "On adjoint operators for fractional differentiation operators." Russian Universities Reports. Mathematics, no. 131 (2020): 284–89. http://dx.doi.org/10.20310/2686-9667-2020-25-131-284-289.

Texte intégral

Résumé :

On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation. Similar results are established for the Riemann–Liouville fractional differentiation operators. We also demonstrate that the operator, which is represented as the sum of the left-sided and the right-sided fractional differentiation operators is self adjoint. The known properties of the Caputo and Riemann–Liouville fractional derivatives are used to substantiate the results.

Styles APA, Harvard, Vancouver, ISO, etc.

7

Chii-Huei, Yu. "Study of Two Matrix Fractional Integrals by Using Differentiation under Fractional Integral Sign." International Journal of Civil and Structural Engineering Research 12, no. 2 (2024): 24–30. https://doi.org/10.5281/zenodo.14039724.

Texte intégral

Résumé :

Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional integral, we find the exact solutions of two matrix fractional integrals. Differentiation under fractional integral sign and a new multiplication of fractional analytic functions play important roles in this article. In fact, our results are generalizations of classical calculus results.  Keywords: Jumarie type of R-L fractional integral, matrix fractional integrals, differentiation under fractional integral sign, new multiplication, fractional analytic functions. Title: Study of Two Matrix Fractional Integrals by Using Differentiation under Fractional Integral Sign Author: Chii-Huei Yu International Journal of Civil and Structural Engineering Research   ISSN 2348-7607 (Online) Vol. 12, Issue 2, October 2024 - March 2025 Page No: 24-30 Research Publish Journals Website: www.researchpublish.com Published Date: 05-November-2024 DOI: https://doi.org/10.5281/zenodo.14039724 Paper Download Link (Source) https://www.researchpublish.com/papers/study-of-two-matrix-fractional-integrals-by-using-differentiation-under-fractional-integral-sign

Styles APA, Harvard, Vancouver, ISO, etc.

8

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.

Texte intégral

Résumé :

Abstract: 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. Keywords: Jumarie’s modified R-L fractional calculus, new multiplication, fractional analytic functions, improper fractional integral, differentiation under fractional integral sign, integration by parts for fractional calculus. Title: Solving Some Type of Improper Fractional Integral Using Differentiation under Fractional Integral Sign and Integration by Parts for Fractional Calculus Author: Chii-Huei Yu, Kuang-Wu Yang International Journal of Engineering Research and Reviews ISSN 2348-697X (Online) Vol. 12, Issue 4, October 2024 - December 2024 Page No: 34-38 Research Publish Journals Website: www.researchpublish.com Published Date: 16-October-2024 DOI: https://doi.org/10.5281/zenodo.13939320 Paper Download Link (Source) https://www.researchpublish.com/papers/solving-some-type-of-improper-fractional-integral-using-differentiation-under-fractional-integral-sign-and-integration-by-parts-for-fractional-calculus

Styles APA, Harvard, Vancouver, ISO, etc.

9

Atangana, Abdon, and Ilknur Koca. "New direction in fractional differentiation." Mathematics in Natural Science 01, no. 01 (2017): 18–25. http://dx.doi.org/10.22436/mns.01.01.02.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

10

Hào, Dinh Nho, and Mai Thi Thu. "Stability results for fractional differentiation." Applicable Analysis 76, no. 3-4 (2000): 249–60. http://dx.doi.org/10.1080/00036810008840881.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

11

Oustaloup, A., B. Orsoni, P. Melchior, and H. Linarès. "Path planning by fractional differentiation." Robotica 21, no. 1 (2003): 59–69. http://dx.doi.org/10.1017/s0263574702004319.

Texte intégral

Résumé :

In path planning design, potential fields can introduce force constraints to ensure curvature continuity of trajectories and thus facilitate path-tracking design. The parametric thrift of fractional potentials permits smooth variations of the potential in function of the distance to obstacles without requiring design of geometric charge distribution. In the approach we use, the fractional order of differentiation is the risk coefficient associated to obstacles. A convex danger map towards a target and a convex geodesic distance map are defined. Real-time computation can also lead to the shortest minimum danger trajectory, or to the least dangerous of minimum length trajectories.

Styles APA, Harvard, Vancouver, ISO, etc.

12

Mathieu, B., P. Melchior, A. Oustaloup, and Ch Ceyral. "Fractional differentiation for edge detection." Signal Processing 83, no. 11 (2003): 2421–32. http://dx.doi.org/10.1016/s0165-1684(03)00194-4.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

13

Schellnhuber, H. J., and A. Seyler. "Fractional differentiation of devil's staircases." Physica A: Statistical Mechanics and its Applications 191, no. 1-4 (1992): 491–500. http://dx.doi.org/10.1016/0378-4371(92)90573-9.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

14

Li, Wenbin, Hongjun Ma, and Tinggang Zhao. "Construction of Fractional Pseudospectral Differentiation Matrices with Applications." Axioms 13, no. 5 (2024): 305. http://dx.doi.org/10.3390/axioms13050305.

Texte intégral

Résumé :

Differentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators. Fractional differentiation of Jacobi orthogonal polynomials can be expressed explicitly through Jacobi–Jacobi transformations between two indexes. In the current paper, an algorithm is presented to construct a fractional differentiation matrix with a matrix representation for Riemann–Liouville, Caputo and Riesz derivatives, which makes the computation stable and efficient. Applications of the fractional differentiation matrix with the spectral collocation method to various problems, including fractional eigenvalue problems and fractional ordinary and partial differential equations, are presented to show the effectiveness of the presented method.

Styles APA, Harvard, Vancouver, ISO, etc.

15

Park, Sungbum, and Seongik Han. "Robust Backstepping Control Combined with Fractional-Order Tracking Differentiator and Fractional-Order Nonlinear Disturbance Observer for Unknown Quadrotor UAV Systems." Applied Sciences 12, no. 22 (2022): 11637. http://dx.doi.org/10.3390/app122211637.

Texte intégral

Résumé :

In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A fractional-order filtered error and a fractional-order tracking differentiator were utilized in a conventional BSC system to improve the positioning control performance of a highly coupled nonlinear quadrotor UAV system and bypass the differentiation issue of the virtual control and compensation of the transformation error in the conventional BSC design. A new fractional-order disturbance observer with the sine hyperbolic function was then proposed to enhance the estimation performance of the uncertain quadrotor UAV. Sequential comparative simulations were conducted, demonstrating that the proposed positioning controller and observer utilizing fractional-order calculus outperformed those of the conventional controller and observer systems.

Styles APA, Harvard, Vancouver, ISO, etc.

16

Figueiredo Camargo, R., Ary O. Chiacchio, and E. Capelas de Oliveira. "Differentiation to fractional orders and the fractional telegraph equation." Journal of Mathematical Physics 49, no. 3 (2008): 033505. http://dx.doi.org/10.1063/1.2890375.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

17

Gholami, Saeid, Esmail Babolian, and Mohammad Javidi. "Fractional pseudospectral integration/differentiation matrix and fractional differential equations." Applied Mathematics and Computation 343 (February 2019): 314–27. http://dx.doi.org/10.1016/j.amc.2018.08.044.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

18

Benkhettou, Nadia, Artur M. C. Brito da Cruz, and Delfim F. M. Torres. "A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration." Signal Processing 107 (February 2015): 230–37. http://dx.doi.org/10.1016/j.sigpro.2014.05.026.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

19

Yakhshiboev, Makhdior. "ON THE HADAMARD AND MARCHAUD-HADAMARD-TYPES MIXED FRACTIONAL INTEGRO-DIFFERENTIATION." Eurasian Mathematical Journal 14, no. 4 (2023): 69–91. http://dx.doi.org/10.32523/2077-9879-2023-14-4-69-91.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

20

Barakaev, Dilshod. "MIXED FRACTIONAL INTEGRATION AND DIFFERENTIATION AS RECIPROCAL OPERATIONS." Chronos: natural and technical sciences 6, no. 2(35) (2021): 22–29. http://dx.doi.org/10.52013/2712-9691-35-2-6.

Texte intégral

Résumé :

We study the question of the composition of the mixed fractional integral and the mixed fractional derivative in sufficiently broad class of functions. The treatment formula for mixed fractional derivative is obtained.

Styles APA, Harvard, Vancouver, ISO, etc.

21

Akhmedov, Mumtoz, and Tulkin Mamatov. "Mixed Fractional Integration and Differentiation as Reciprocal Operations." International Journal of Case Studies (ISSN Online 2305-509X) o8, no. 11 (2019): 123–29. https://doi.org/10.5281/zenodo.4841097.

Texte intégral

Résumé :

We study the question of the composition of the mixed fractional integral and the mixed fractional derivative in a sufficiently broad class of functions. The treatment formula for the mixed fractional derivative is obtained

Styles APA, Harvard, Vancouver, ISO, etc.

22

Kukushkin, M. V. "ON SOME QUALITATIVE PROPERTIES OF THE OPERATOR OF FRACTIONAL DIFFERENTIATION IN KIPRIYANOV SENSE." Vestnik of Samara University. Natural Science Series 23, no. 2 (2017): 32–43. http://dx.doi.org/10.18287/2541-7525-2017-23-2-32-43.

Texte intégral

Résumé :

In this paper we investigated the qualitative properties of the operator of fractional differentiation in Kipriyanov sense. Based on the concept of multidimensional generalization of operator of fractional differentiation in Marchaud sense we have adapted earlier known techniques of proof theorems of one-dimensional theory of fractional calculus for the operator of fractional differentiation in Kipriyanov sense. Along with the previously known definition of the fractional derivative in the direction we used a new definition of multidimensional fractional integral in the direction of allowing you to expand the domain of definition of formally adjoint operator. A number of theorems that have analogs in one-dimensional theory of fractional calculus is proved. In particular the sufficient conditions of representability of a fractional integral in the direction are received. Integral equality the result of which is the construction of the formal adjoint operator defined on the set of functions representable by the fractional integral in direction is proved.

Styles APA, Harvard, Vancouver, ISO, etc.

23

Wu, Zhongshu, Xinxia Zhang, Jihan Wang, and Xiaoyan Zeng. "Applications of Fractional Differentiation Matrices in Solving Caputo Fractional Differential Equations." Fractal and Fractional 7, no. 5 (2023): 374. http://dx.doi.org/10.3390/fractalfract7050374.

Texte intégral

Résumé :

This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the fractional differentiation matrices for Caputo fractional derivatives. With the fractional differentiation matrices, the fractional differential equations were transformed into linear systems, which are easier to solve. Two types of fractional differential equations were used for the numerical simulations, and the numerical results demonstrated the fast convergence and high accuracy of the proposed methods.

Styles APA, Harvard, Vancouver, ISO, etc.

24

Bogatyreva, F. T. "On the correctness of initial problems for the fractional diffusion equation." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 23, no. 4 (2023): 16–22. http://dx.doi.org/10.47928/1726-9946-2023-23-4-16-22.

Texte intégral

Résumé :

The paper studies a second-order parabolic partial differential equation with fractional differentiation with respect to a time variable. The fractional differentiation operator is a linear combination of the Riemann-Liouville and Gerasimov-Caputo fractional derivatives. It is shown that the distribution of orders of fractional derivatives, included in the equation affects the correctness of the initial problems for the equation under consideration.

Styles APA, Harvard, Vancouver, ISO, etc.

25

TATOM, FRANK B. "THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS." Fractals 03, no. 01 (1995): 217–29. http://dx.doi.org/10.1142/s0218348x95000175.

Texte intégral

Résumé :

The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).

Styles APA, Harvard, Vancouver, ISO, etc.

26

Alexopoulos, Aris. "Dualities and Asymptotic Mixtures Using Functional-Order Differentiation." AppliedMath 2, no. 3 (2022): 359–78. http://dx.doi.org/10.3390/appliedmath2030021.

Texte intégral

Résumé :

New definitions for fractional integro-differential operators are presented and referred to as delayed fractional operators. It is shown that delayed fractional derivatives give rise to the notion of functional order differentiation. Functional differentiation can be used to establish dualities and asymptotic mixtures between unrelated theories, something that conventional fractional or integer operators cannot do. In this paper, dualities and asymptotic mixtures are established between arbitrary functions, probability densities, the Gibbs–Shannon entropy and Hellinger distance, as well as higher-dimensional particle geometries in quantum mechanics.

Styles APA, Harvard, Vancouver, ISO, etc.

27

Gautam, Pranjali, Harish Nagar, and Sonia Sharma. "The Marichev-Saigo-Maeda fractional calculus operator pertaining to the generalized multivariate Mittag-Leffler function." Journal of Interdisciplinary Mathematics 27, no. 8 (2024): 1853–60. https://doi.org/10.47974/jim-2050.

Texte intégral

Résumé :

The objective of this paper is to explore and establish certain generalized fractional differentiation and integration involving multivariate generalized Mittag-Leffler function introduced by Salim and Faraz. The generalization of Saigo fractional calculus operators that is Marichev-Saigo-Maeda Fractional Calculus Operator is utilized to establish some formulas related to generalized multivariate M-L function. In conclusion, we depict some key characteristics of generalized fractional integrals and differentiation pertaining to Generalized Multivariate Mittag- Leffler Function.

Styles APA, Harvard, Vancouver, ISO, etc.

28

Lundstrom, Brian N., Matthew H. Higgs, William J. Spain, and Adrienne L. Fairhall. "Fractional differentiation by neocortical pyramidal neurons." Nature Neuroscience 11, no. 11 (2008): 1335–42. http://dx.doi.org/10.1038/nn.2212.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

29

Gao, Chaobang, Jiliu Zhou, Weihua Zhang, and Mei Gong. "Generalized Fractional Differentiation and Its Applications." Journal of Computational and Theoretical Nanoscience 10, no. 4 (2013): 867–83. http://dx.doi.org/10.1166/jctn.2013.2783.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

30

Xu, Xiangwei, Fang Dai, Jianmin Long, and Wenyan Guo. "Fractional Differentiation-based Image Feature Extraction." International Journal of Signal Processing, Image Processing and Pattern Recognition 7, no. 6 (2014): 51–64. http://dx.doi.org/10.14257/ijsip.2014.7.6.05.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

31

Baleanu, Dumitru, and J. A. Tenreiro Machado. "Fractional Differentiation and its Applications (FDA08)." Physica Scripta T136 (October 2009): 011001. http://dx.doi.org/10.1088/0031-8949/2008/t136/011001.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

32

Zhao, Jingjun, Teng Long, and Yang Xu. "High order fractional backward differentiation formulae." Applicable Analysis 96, no. 10 (2016): 1669–80. http://dx.doi.org/10.1080/00036811.2016.1257124.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

33

Hào, Dinh Nho, H. J. Reinhardt, and F. Seiffarth. "Stable nunerical fractional differentiation by mollification." Numerical Functional Analysis and Optimization 15, no. 5-6 (1994): 635–59. http://dx.doi.org/10.1080/01630569408816585.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

34

Baleanu, Dumitru, J. A. Tenreiro Machado, and Wen Chen. "Fractional differentiation and its applications I." Computers & Mathematics with Applications 66, no. 5 (2013): 575. http://dx.doi.org/10.1016/j.camwa.2013.06.006.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

35

Metwally, M. S., Lalit Mohan Upadhyaya, S. Abo-Hasha, and Karima Hamza. "A study of the k-Horn’s hypergeometric function H9,k∗." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 42, no. 2 (2023): 126–42. http://dx.doi.org/10.48165/bpas.2023.42e.2.4.

Texte intégral

Résumé :

In this paper, we introduce the k-Horn’s hypergeometric function H9,k and we investigate its limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, the Laplace, Mellin, fractional Fourier, double Laplace and double Mellin transforms for the k-Horn’s hypergeometric function H9,k. Finally, we discuss the fractional integration and the k-fractional differentiation .

Styles APA, Harvard, Vancouver, ISO, etc.

36

Chii-Huei, Yu. "Using Differentiation under Fractional Integral Sign to Solve Three Types of Fractional Integrals." International Journal of Computer Science and Information Technology Research 12, no. 4 (2024): 26–33. https://doi.org/10.5281/zenodo.14016985.

Texte intégral

Résumé :

Abstract: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional integral and a new multiplication of fractional analytic functions, we can find three types of fractional integrals. In fact, our results are generalizations of classical calculus results. Keywords: Jumarie’s modified R-L fractional integral, new multiplication, fractional analytic functions, fractional integrals. Title: Using Differentiation under Fractional Integral Sign to Solve Three Types of Fractional Integrals Author: Chii-Huei Yu International Journal of Computer Science and Information Technology Research ISSN 2348-1196 (print), ISSN 2348-120X (online) Vol. 12, Issue 4, October 2024 - December 2024 Page No: 26-33 Research Publish Journals Website: www.researchpublish.com Published Date: 31-October-2024 DOI: https://doi.org/10.5281/zenodo.14016985 Paper Download Link (Source) https://www.researchpublish.com/papers/using-differentiation-under-fractional-integral-sign-to-solve-three-types-of-fractional-integrals

Styles APA, Harvard, Vancouver, ISO, etc.

37

Khan, Waseem Ahmad, Hassen Aydi, Musharraf Ali, Mohd Ghayasuddin, and Jihad Younis. "Construction of Generalized k-Bessel–Maitland Function with Its Certain Properties." Journal of Mathematics 2021 (November 20, 2021): 1–14. http://dx.doi.org/10.1155/2021/5386644.

Texte intégral

Résumé :

The main motive of this study is to present a new class of a generalized k -Bessel–Maitland function by utilizing the k -gamma function and Pochhammer k -symbol. By this approach, we deduce a few analytical properties as usual differentiations and integral transforms (likewise, Laplace transform, Whittaker transform, beta transform, and so forth) for our presented k -Bessel–Maitland function. Also, the k -fractional integration and k -fractional differentiation of abovementioned k -Bessel–Maitland functions are also pointed out systematically.

Styles APA, Harvard, Vancouver, ISO, etc.

38

Ivanova, Elena, Xavier Moreau, and Rachid Malti. "Stability and resonance conditions of second-order fractional systems." Journal of Vibration and Control 24, no. 4 (2016): 659–72. http://dx.doi.org/10.1177/1077546316654790.

Texte intégral

Résumé :

The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

Styles APA, Harvard, Vancouver, ISO, etc.

39

Benmahmoud, Slimane. "Some theoretical results on fractional-order continuous information measures." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 23, no. 1 (2024): 5–12. http://dx.doi.org/10.2478/aupcsm-2024-0001.

Texte intégral

Résumé :

Abstract By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation α → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.

Styles APA, Harvard, Vancouver, ISO, etc.

40

Huang, Tingsheng, Xinjian Wang, Da Xie, Chunyang Wang, and Xuelian Liu. "Depth Image Enhancement Algorithm Based on Fractional Differentiation." Fractal and Fractional 7, no. 5 (2023): 394. http://dx.doi.org/10.3390/fractalfract7050394.

Texte intégral

Résumé :

Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image−enhancement methods, which are typically based on integer−order calculus, cannot exploit the textural information of an image, and their enhancement effect is limited. To solve this problem, fractional differentiation has been introduced as an innovative image−processing tool. It enables the flexible use of local and non−local information by taking into account the continuous changes between orders, thereby improving the enhancement effect. In this study, a fractional differential is applied in depth image enhancement and used to establish a novel algorithm, named the fractional differential–inverse−distance−weighted depth image enhancement method. Experiments are performed to verify the effectiveness and universality of the algorithm, revealing that it can effectively solve edge and hole interference and significantly enhance textural details. The effects of the order of fractional differentiation and number of iterations on the enhancement performance are examined, and the optimal parameters are obtained. The process data of depth image enhancement associated with the optimal number of iterations and fractional order are expected to facilitate depth image enhancement in actual scenarios.

Styles APA, Harvard, Vancouver, ISO, etc.

41

LEUNG, A. Y. T., and ZHONGJIN GUO. "EFFECTS OF FRACTIONAL DIFFERENTIATION ORDERS ON A COUPLED DUFFING CIRCUIT." International Journal of Bifurcation and Chaos 23, no. 12 (2013): 1350193. http://dx.doi.org/10.1142/s0218127413501939.

Texte intégral

Résumé :

Classical electrical circuits consist of resistors and capacitors and are governed by integer-order model. Circuits may have so-called fractance which represents an electrical element with fractional order impedance. Therefore, fractional order derivative is important to study the dynamical behaviors of circuits. This paper extends the classical coupled Duffing circuits to cover a new fractional order Duffing system consisting of two identical periodic forced circuits coupled by a linear resistor. The fundamental resonance responses under various paired and unpaired fractional orders are investigated in detail using the harmonic balance in combination with polynomial homotopy continuation. The approximate solutions having a high degree of accuracy in the steady state response are sought. There exist different shapes of frequency versus response and excitation amplitude versus response curves under various fractional orders. Multiple-valued solutions and nonclassical bifurcations are observed analytically and verified numerically. The influence of coupling intensity on the fundamental resonance response is also examined. New contributions include the innovative introduction of fractional order to the coupled Duffing circuits, the explicit integration of fractional order and the linear consideration of higher harmonics to improve the nonlinear solutions of the lower harmonics without increasing the computational complexity.

Styles APA, Harvard, Vancouver, ISO, etc.

42

Liu, D. Y., T. M. Laleg-Kirati, and O. Gibaru. "Fractional order differentiation by integration: an application to fractional linear systems." IFAC Proceedings Volumes 46, no. 1 (2013): 653–58. http://dx.doi.org/10.3182/20130204-3-fr-4032.00208.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

43

Litovchenko, V. "POST'S PSEUDO-DIFFERENTIAL OPERATOR IN S-TYPE SPACES." Bukovinian Mathematical Journal 11, no. 2 (2023): 153–61. http://dx.doi.org/10.31861/bmj2023.02.15.

Texte intégral

Résumé :

During the last few decades, the theory of fractional differentiation and pseudo-differential operators, which naturally generalize and extend the concepts of classical derivative and differential operations, has been rapidly developing. The reason for this development is primarily the close connection of pseudo-differential operators and fractional differentiation with important problems of analysis and modern mathematical physics. It turned out that such player operators play an important role in the theory of analytical boundary-value problems (in the study of the index of the problem, in reduction to the boundary of the region, etc.), in microlocal analysis, in the theory of random processes, with the help of fractal differentiation operators heat-diffusive processes in porous media, etc. There are different approaches to the generalization of the classical derivative, the implementation of which gave rise to a variety of fractional differentiation and pseudodifferentiation operations. In this connection, there is a natural need for a comparative characterization of these generalizations, which is convenient to conduct through the prism of the classical form of fractional differentiation on elements with "sufficiently good" properties. In addition, the representation of this or that pseudo-differentiation operation in such a classical form makes it possible to use a rather convenient Fourier transform apparatus for the analysis of problems with these operations. In this work, the question of the possibility of representation in S type spaces of I.M. Gelfand is investigated. and Shilova G.E. pseudo-differential operator E. Post a(Dx) in the classical form of fractional differentiation, provided that its symbol a(·) is a convolution in the original space.

Styles APA, Harvard, Vancouver, ISO, etc.

44

Tarasov, Vasily E., and Valentina V. Tarasova. "Long and Short Memory in Economics: Fractional-Order Difference and Differentiation." IRA-International Journal of Management & Social Sciences (ISSN 2455-2267) 5, no. 2 (2016): 327. http://dx.doi.org/10.21013/jmss.v5.n2.p10.

Texte intégral

Résumé :

<div>Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov fractional differences of non-integer order d. Equations of ARIMA(p,d,q) and ARFIMA(p,d,q) models are the fractional-order difference equations with the Grunwald-Letnikov differences of order d. We prove that the long and short memory with power law should be described by the exact fractional-order differences, for which the Fourier transform demonstrates the power law exactly. The fractional differencing and the Grunwald-Letnikov fractional differences cannot give exact results for the long and short memory with power law, since the Fourier transform of these discrete operators satisfy the power law in the neighborhood of zero only. We prove that the economic processes with the continuous time long and short memory, which is characterized by the power law, should be described by the fractional differential equations.</div>

Styles APA, Harvard, Vancouver, ISO, etc.

45

Chii-Huei, Yu. "Solution of Some Type of Improper Fractional Integral." International Journal of Interdisciplinary Research and Innovations 11, no. 1 (2023): 11–16. https://doi.org/10.5281/zenodo.7536528.

Texte intégral

Résumé :

Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral. Differentiation under fractional integral sign and a new multiplication of fractional analytic functions play important roles in this paper. Moreover, some examples are given to illustrate our main result. In fact, our result is a generalization of ordinary calculus result.  Keywords: Jumarie type of R-L fractional calculus, improper fractional integral, differentiation under fractional integral sign, new multiplication, fractional analytic functions. Title: Solution of Some Type of Improper Fractional Integral Author: Chii-Huei Yu International Journal of Interdisciplinary Research and Innovations ISSN 2348-1218 (print), ISSN 2348-1226 (online) Vol. 11, Issue 1, January 2023 - March 2023 Page No: 11-16 Research Publish Journals Website: www.researchpublish.com Published Date: 14-January-2023 DOI: https://doi.org/10.5281/zenodo.7536528 Paper Download Link (Source) https://www.researchpublish.com/papers/solution-of-some-type-of-improper-fractional-integral

Styles APA, Harvard, Vancouver, ISO, etc.

46

Yuan, Shanhao, Yanqin Liu, Yibin Xu, Qiuping Li, Chao Guo, and Yanfeng Shen. "Gradient-enhanced fractional physics-informed neural networks for solving forward and inverse problems of the multiterm time-fractional Burger-type equation." AIMS Mathematics 9, no. 10 (2024): 27418–37. http://dx.doi.org/10.3934/math.20241332.

Texte intégral

Résumé :

In this paper, we introduced the gradient-enhanced fractional physics-informed neural networks (gfPINNs) for solving the forward and inverse problems of the multiterm time-fractional Burger-type equation. The gfPINNs leverage gradient information derived from the residual of the fractional partial differential equation and embed the gradient into the loss function. Since the standard chain rule in integer calculus is invalid in fractional calculus, the automatic differentiation of neural networks does not apply to fractional operators. The automatic differentiation for the integer order operators and the finite difference discretization for the fractional operators were used to construct the residual in the loss function. The numerical results demonstrate the effectiveness of gfPINNs in solving the multiterm time-fractional Burger-type equation. By comparing the experimental results of fractional physics-informed neural networks (fPINNs) and gfPINNs, it can be seen that the training performance of gfPINNs is better than fPINNs.

Styles APA, Harvard, Vancouver, ISO, etc.

47

Zhang, Yiqun, Honglei Xu, Yang Li, et al. "An Integer-Fractional Gradient Algorithm for Back Propagation Neural Networks." Algorithms 17, no. 5 (2024): 220. http://dx.doi.org/10.3390/a17050220.

Texte intégral

Résumé :

This paper proposes a new optimization algorithm for backpropagation (BP) neural networks by fusing integer-order differentiation and fractional-order differentiation, while fractional-order differentiation has significant advantages in describing complex phenomena with long-term memory effects and nonlocality, its application in neural networks is often limited by a lack of physical interpretability and inconsistencies with traditional models. To address these challenges, we propose a mixed integer-fractional (MIF) gradient descent algorithm for the training of neural networks. Furthermore, a detailed convergence analysis of the proposed algorithm is provided. Finally, numerical experiments illustrate that the new gradient descent algorithm not only speeds up the convergence of the BP neural networks but also increases their classification accuracy.

Styles APA, Harvard, Vancouver, ISO, etc.

48

Qian, Ailin. "Numerical Fractional Differentiation: Stability Estimate and Regularization." British Journal of Mathematics & Computer Science 3, no. 3 (2013): 448–57. http://dx.doi.org/10.9734/bjmcs/2013/3921.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

49

Sabatier, Jocelyn, Mathieu Merveillaut, Junior Mbala Francisco, Franck Guillemard, and Denis Porcelatto. "Lithium-ion batteries modeling involving fractional differentiation." Journal of Power Sources 262 (September 2014): 36–43. http://dx.doi.org/10.1016/j.jpowsour.2014.02.071.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

50

Ferdi, Y., J. P. Herbeuval, A. Charef, and B. Boucheham. "R wave detection using fractional digital differentiation." ITBM-RBM 24, no. 5-6 (2003): 273–80. http://dx.doi.org/10.1016/j.rbmret.2003.08.002.

Texte intégral

Styles APA, Harvard, Vancouver, ISO, etc.

Articles de revues sur le sujet « Fractional differentiation »

Créez une référence correcte selon les styles APA, MLA, Chicago, Harvard et plusieurs autres