Existence and uniqueness of positive solutions for a Hadamard fractional integral boundary value problem

The main aim of this paper is to study a kind of boundary value problem with an integral boundary condition including Hadamard-type fractional differential equations. To do this, upper and lower solutions are used to guarantee their existence, and Schauder’s fixed point theorem is used to prove the uniqueness of the positive solutions to this problem. An illustrated example is presented to explain the theorems that have been proved.

Keywords:

Hadamard fractional derivative , Boundary value problem , Integral Boundary Condition