Open Access

ARTICLE

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

Fairouz Tchier¹, Hassan Khan^2,3,*, Shahbaz Khan², Poom Kumam^4,5, Ioannis Dassios⁶
1 Mathematics Department, King Saudi University, Riyadh, 145111, Saudi Arabia
2 Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Pakistan
3 Department of Mathematics, Near East University, Nicosia, 99138, Turkey
4 Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand
5 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
6 AMPSAS, University College Dublin, Dublin, A94 XF34, Ireland
* Corresponding Author: Hassan Khan. Email:
(This article belongs to this Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2137-2153. https://doi.org/10.32604/cmes.2023.022855

Received 29 March 2022; Accepted 01 July 2022; Issue published 23 November 2022

Abstract

The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems.

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Keywords

Fractional calculus; laplace transform; laplace residual power series method; fractional partial differential equation; power series; fractional power series

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