Numerical solution of fuzzy fractional integro-differential equation via two-dimensional Legendre Wavelet method

Article type: Research Article

Authors: Shabestari, Mohammad Rasul Mastani^a | Ezzati, Reza^{b; *} | Allahviranloo, Tofigh^a

Affiliations: [a] Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran | [b] Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Correspondence: [*] Corresponding author. Reza Ezzati, Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. E-mail: [email protected].

Abstract: In this paper, the two-dimensional Legendre wavelet is studied to approximated the solution of fuzzy fractional integro-differential equation under Caputo generalized Hukuhara differentiability. The existence and uniqueness theorems for a fuzzy fractional integro-differential equation by considering the type of differentiability of solution are proved. Furthermore, the accuracy and efficiency of the proposed method are demonstrated is a series of numerical experiments.

Keywords: Fuzzy fractional integro-differential equation, Caputo generalized Hukuhara differentiability, Legendre wavelet method

DOI: 10.3233/JIFS-171707

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2453-2465, 2018