Comparative analysis of fractional dynamical systems with various operators

Qasim Khan; Anthony Suen; Hassan Khan; Poom Kumam; Qasim Khan; Anthony Suen; Hassan Khan; Poom Kumam

doi:10.3934/math.2023714

AIMS Mathematics

2023, Volume 8, Issue 6: 13943-13983. doi: 10.3934/math.2023714

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Comparative analysis of fractional dynamical systems with various operators

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

Received: 25 December 2022 Revised: 02 March 2023 Accepted: 09 March 2023 Published: 13 April 2023
MSC : 26A33, 34A08

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.
- new iterative transform method,
- Navier Stokes equation,
- Cauchy equation,
- Atangana-Baleanu operator,
- Caputo operator,
- Caputo-Fabrizio operator,
- Aboodh transformation
Citation: Qasim Khan, Anthony Suen, Hassan Khan, Poom Kumam. Comparative analysis of fractional dynamical systems with various operators[J]. AIMS Mathematics, 2023, 8(6): 13943-13983. doi: 10.3934/math.2023714

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Abstract

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.

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