Boundary Value Problems of Hadamard-Type Fractional Differential Equations and Inclusions with Nonlocal Conditions

Abstract

In this paper, we obtain some new existence and uniqueness results for boundary value problems of Hadamard type fractional differential equations and inclusions with nonlocal boundary conditions. The contraction mapping principle and a fixed point theorem due to O’Regan are the main tools of our study for the single-valued case, while the multi-valued case is based on the nonlinear alternative for contractive maps. The results are well illustrated with the aid of examples.