Existence of solutions for conformable fractional problems with nonlinear functional boundary conditions

Abstract

In this article, we study the existence of solutions for nonlinear conformable fractional differential equations with nonlinear functional boundary conditions. We obtain the exact expression of the fractional Green’s function related to the linear problem. Moreover, the method of upper and lower solutions together with Schauder’s fixed point theorem is developed for the nonlinear conformable fractional problems with nonlinear functional boundary conditions.