Nonlinear Hadamard fractional boundary value problems with different orders

Abstract

In this paper, we study the existence (uniqueness) of solutions for nonlinear fractional differential equations with different orders of Hadamard fractional derivatives involving associated with nonlocal boundary conditions. Several fixed point theorems are used for sufficient conditions of the existence (uniqueness) of solutions to nonlinear differential equations such as Banach’s contraction principle, the Leray–Schauder nonlinear alternative, and Krasnoselskii’s fixed point theorem. Applications of the main results are also presented.