On the existence and uniqueness results for fuzzy fractional boundary value problem involving Caputo iractional derivative

Abstract

In this paper, we investigate the existence and uniqueness of solutions for fuzzy boundary value problems involving fuzzy Caputo fractional derivatives of order q 2 (2, 3). As a preliminary step, we construct a generic structure of the solution associated with our proposed model by utilizing the Green’s function. We establish the existence of a unique solution of the proposed model paired with the given initial conditions by using Banach fixed point theorem. At last, as application, an illustrative example is given to show the applicability of our theoritical results.