A fuzzy solution of nonlinear partial differential equations of fractional order

Author(s): Mawia Osman1,2, Ahmed Hamoud3, Altyeb Mohammed Mustafa4, Zengtai Gong2, Bchir Mahamat Acyl2, Abdoulaye Ali2, Bakry Musa2
1College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, P.R. China.
2College of Mathematics and Statistics, Northwest Normal University, Lanzhou, P.R. China.
3Department of Mathematics, Taiz University, Taiz, Yemen.
4Department of Applied Mathematics, Faculty of Mathematical Science, University of Khartoum, Khartoum, Sudan.
Copyright © Mawia Osman, Ahmed Hamoud, Altyeb Mohammed Mustafa, Zengtai Gong, Bchir Mahamat Acyl, Abdoulaye Ali, 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.

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:

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