Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition
The main purpose of this paper is to present the existence results of solutions and positive solutions of nonlinear high-order fractional boundary value problems with integral boundary condition. By using the Banach fixed point theorem and the Krasnoselskii fixed point theorem, we obtain the existence and uniqueness of real solution. By the GuoKrasnoselskii fixed point theorem on the cone, we obtain a desired result for guaranteeing the existence of positive solution. Several interesting examples relevant to the main results are also considered.
boundary value problem positive solution fixed point theorem fractional differential equations fractional calculus 26a33 34a08