Outcomes for The Analysis of The Existence of Fuzzy Fractional Differential Equations

Abstract

In this article, a Cauchy problem for a fuzzy q-fractional differential equation of order α has been considered.The results for generalized Hukuhara q-differentiablity of a fuzzy function are established. This work has led to the study of existence and uniqueness of the fuzzy function with Caputo Hukuhara q-differentiability and generalized Banach fixed point theorem. A crucial qualitative property of the differential equation, which is continuous dependence on initial conditions and the functions involved is analysed. An illustrative example is given which ensures the result.