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.
