New Existence Results for Nonlinear Fractional Differential Equations with Three-Point Integral Boundary Conditions

Abstract

This paper studies a boundary value problem of nonlinear fractional differential equations of order with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears in the integral part of the conditions in contrast to the available literature on three-point boundary value problems which deals with the three-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are also discussed.