Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

Abstract

We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)), t∈[0,1], u(0)=0, u′(0)+u′′(0)=0, u′(1)+u′′(1)=0, where α∈(2,3] is a real number, CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.