Semi-analytical methods for solving fuzzy impulsive fractional differential equations

Article type: Research Article

Authors: Najafi, Nematallah^a | Allahviranloo, Tofigh^{b; *}

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

Correspondence: [*] Corresponding author. Tofigh Allahviranloo, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. E-mail: [email protected].

Abstract: In this paper, we study semi-analytical methods entitled fuzzy fractional differential transform method to solve fuzzy impulsive fractional differential equations using Caupto fractional derivative. At the end first of all fuzzy differential transform method in fractional case is defined and its properties are considered completely. Then existence and uniquness theorem for the solution are proved and convergence of the proposed method is considered in details. Some examples indicate that this method can be easily applied to many linear and nonlinear problems.

Keywords: Fractional differential transform method, fuzzy impulsive fractional differential, generalized Hukuhara differentiability

DOI: 10.3233/JIFS-17190

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3539-3560, 2017