EXISTENCE AND ULAM STABILITY OF SOLUTIONS FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING TWO FRACTIONAL ORDERS

Abstract

In this paper, we study existence, uniqueness and Ulam-Hyers stability of solutions for integro-differential equations involving two fractional orders. By using Banach's fixed point theorem, we obtain some sufficient conditions for the existence and uniqueness of solution for the mentioned problem. Furthermore, we derive the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solution. At the end, an illustrative example is discussed.