EXISTENCE OF SOLUTIONS AND ULAM STABILITY OF HILFER-HADAMARD SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM

In this paper, we study the existence and uniqueness of solutions for the boundary value problem of Hilfer-Hadamard sequential fractional differential equations via fixed point theorems. The existence of a solution is proved by the Krasnoselskii fixed point theorem, the Leray-Schauder alternative, and the Leray-Schauder nonlinear alternative fixed point theorem. Moreover, we prove the uniqueness of the solution using the Banach contraction principle. We also discuss the Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers and generalized Ulam-Hyers-Rassias stability for the problem. Illustrative examples are also provided.