Open Journal of Discrete Applied Mathematics

Vol. 5 (2022), Issue 3, pp. 13 – 29
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2022.0076

A fuzzy solution of nonlinear partial differential equations of fractional order

Mawia Osman\(^{1,2,*}\), Ahmed Hamoud\(^{3,*}\), Altyeb Mohammed Mustafa\(^{4}\), Zengtai Gong \(^{2}\), Bchir Mahamat Acyl\(^{2}\), Abdoulaye Ali\(^{2}\) and Bakry Musa\(^{2}\)
\(^{1}\) College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, P.R. China.
\(^{2}\) College of Mathematics and Statistics, Northwest Normal University, Lanzhou, P.R. China.
\(^{3}\) Department of Mathematics, Taiz University, Taiz, Yemen.
\(^{4}\) Department of Applied Mathematics, Faculty of Mathematical Science, University of Khartoum, Khartoum, Sudan.
Correspondence should be addressed to Mawia Osman at mawiaosman@yahoo.com or Ahmed Hamoud at drahmed985@yahoo.com Tel.: +8615682896302

Copyright © 2022 Mawia Osman, Ahmed Hamoud, Altyeb Mohammed Mustafa, Zengtai Gong, Bchir Mahamat Acyl, Abdoulaye Ali and Bakry Musa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: March 28, 2022 – Accepted: November 20, 2022 – Published: December 31, 2022

Abstract

In this paper, the fuzzy nonlinear partial differential equations of fractional order are considered. The generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) were applied to solve fuzzy nonlinear partial differential equations of fractional order. The above methods are investigated based on Taylor’s formula, and fuzzy Caputo’s fractional derivative. The proposed methods are also illustrated by some examples. The results reveal the methods are a highly effective scheme for obtaining the fuzzy fractional partial differential equations.

Keywords:

Fuzzy numbers; Fuzzy-valued functions; Fuzzy fractional partial differential equations; DTM; VIM; Taylor’s formula; Fuzzy Caputo’s fractional derivative.