Discrete Dynamics in Nature and Society (Jan 2015)
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.