Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

Abstract

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional orderqgiven bycDqx(t)=f(t,x(t)),0<t<1,q∈(m−1,m],m∈ℕ,m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0,x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.