Comparative analysis of fractional dynamical systems with various operators-Reference-Cited by-同舟云学术

Comparative analysis of fractional dynamical systems with various operators

Published:2023 Issue:6 Volume:8 Page:13943-13983
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khan Qasim¹,Suen Anthony¹,Khan Hassan²,Kumam Poom³⁴

Affiliation:

1. Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong

2. Department of Mathematics, Abdul Wali khan University Mardan, Pakistan

3. Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>This article implements an efficient analytical technique within three different operators to investigate the solutions of some fractional partial differential equations and their systems. The generalized schemes of the proposed method are derived for every targeted problem under the influence of each fractional derivative operator. The numerical examples of the non-homogeneous fractional Cauchy equation and three-dimensional Navier-Stokes equations are obtained using the new iterative transform method. The obtained results under different fractional derivative operators are found to be identical. The 2D and 3D plots have confirmed the close connection between the exact and obtained results. Moreover, the table shows the higher accuracy of the proposed method.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference54 articles.

1. B. Cuahutenango-Barro, M. A. Taneco-Hernández, J. F. Gómez-Aguilar, On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel, Chaos Solitons Fract., 115 (2018), 283–299. https://doi.org/10.1016/j.chaos.2018.09.002

2. J. Gómez-Gardenes, V. Latora, Entropy rate of diffusion processes on complex networks, Phys. Rev. E, 78 (2008), 065102. https://doi.org/10.1103/PhysRevE.78.065102

3. B. Elma, E. Misirli, Two reliable techniques for solving conformable space-time fractional PHI-4 model arising in nuclear physics via $beta$-derivative, Rev. Mex. Fis., 67 (2021), 1–6. https://doi.org/10.31349/revmexfis.67.050707

4. V. B. Chaurasia, D. Kumar, Solution of the time-fractional Navier-Stokes equation, Gen. Math. Notes, 4 (2011), 49–59.

5. J. H. He, Nonlinear oscillation with fractional derivative and its applications, Int. Conf. Vibrating Eng., 98 (1998), 288–291.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Application of an efficient analytical technique based on Aboodh transformation to solve linear and non-linear dynamical systems of integro-differential equations;Partial Differential Equations in Applied Mathematics;2024-09

2. Fractional heat transfer DPL model incorporating an exponential Rabotnov kernel to study an infinite solid with a spherical cavity;AIMS Mathematics;2024