Fuzzy fractional differential equations under generalized fuzzy Caputo derivative

Article type: Research Article

Authors: Allahviranloo, T. | Armand, A. | Gouyandeh, Z.

Affiliations: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Note: [] Corresponding author. T. Allahviranloo, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Tel.: +989123508816; Email: tofigh@allahviranloo.com

Abstract: In this paper the fuzzy Caputo fractional differential equation (FCFDE) under the Generalized Hukuhara differentiability is introduced. Also the existence and uniqueness of the solution for a class of fuzzy Caputo fractional differential equation with initial value is studied, and an analytical solution of FCFDE is obtained. The related theorems and properties are proved in detail and the method is illustrated by solving some examples.

Keywords: Fuzzy Caputo fractional differential equations (FCFDEs), Generalized Hukuhara differentiability, Krasnoselskii-Krein condition

DOI: 10.3233/IFS-130831

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 3, pp. 1481-1490, 2014