Positive Solutions of Fractional Order Differential Equations with Integral Boundary Conditions and a Parameter

Abstract

In this study, we consider a fractional order differential equation with integral boundary conditions and a parameter. In the meantime, we investigate the existence and uniqueness of positive solutions. To accomplish the objectives, we determine the Green’s function for the fractional boundary value problem and develop the operator equation by using Green’s function as a kernel. By applying the Guo-Krasnoseliskii fixed-point theorem on a cone, we develop the existence results of at least one positive solution in a Banach space. To verify uniqueness of the solutions, we apply Banach contraction mapping principle. Finally, we provide particular example to illustrate the main result.