Employing the Laplace Residual Power Series Method to Solve (1+1)- and (2+1)-Dimensional Time-Fractional Nonlinear Differential Equations-Reference-Cited by-同舟云学术

Employing the Laplace Residual Power Series Method to Solve (1+1)- and (2+1)-Dimensional Time-Fractional Nonlinear Differential Equations

Published:2024-07-04 Issue:7 Volume:8 Page:401
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Hadhoud Adel R.¹^ORCID,Rageh Abdulqawi A. M.¹²^ORCID,Radwan Taha³⁴^ORCID

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom 32511, Egypt

2. Department of Mathematics and Computer Science, Faculty of Science, Ibb University, Ibb 70270, Yemen

3. Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

4. Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42511, Egypt

Abstract

In this paper, we present a highly efficient analytical method that combines the Laplace transform and the residual power series approach to approximate solutions of nonlinear time-fractional partial differential equations (PDEs). First, we derive the analytical method for a general form of fractional partial differential equations. Then, we apply the proposed method to find approximate solutions to the time-fractional coupled Berger equations, the time-fractional coupled Korteweg–de Vries equations and time-fractional Whitham–Broer–Kaup equations. Secondly, we extend the proposed method to solve the two-dimensional time-fractional coupled Navier–Stokes equations. The proposed method is validated through various test problems, measuring quality and efficiency using error norms E2 and E∞, and compared to existing methods.

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/7/401/pdf

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