A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations-Reference-Cited by-同舟云学术

A Modified Residual Power Series Method for the Approximate Solution of Two-Dimensional Fractional Helmholtz Equations

Published:2023-12-04 Issue:12 Volume:15 Page:2152
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Liu Jinxing¹^ORCID,Nadeem Muhammad²^ORCID,Islam Asad³^ORCID,Mureşan Sorin⁴^ORCID,Iambor Loredana Florentina⁴^ORCID

Affiliation:

1. Faculty of Science, Yibin University, Yibin 644000, China

2. School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, China

3. Department of Mechanical and Aerospace Engineering, Air University, Islamabad 44000, Pakistan

4. Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania

Abstract

In this paper, we suggest a modification for the residual power series method that is used to solve fractional-order Helmholtz equations, which is called the Shehu-transform residual power series method (ST-RPSM). This scheme uses a combination of the Shehu transform (ST) and the residual power series method (RPSM). The fractional derivatives are taken with respect to Caputo order. The novelty of this approach is that it does not restrict the fractional order and reduces the need for heavy computational work. The results were obtained using an iterative series that led to an exact solution. The 3D graphical plots for different values of fractional orders are shown to compare ST-RPSM results with exact solutions.

Funder

University of Oradea

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/12/2152/pdf

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