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 order q given by cDqxt ft, xt , 0 <t< 1, q ∈ m − 1, m , m ∈ N, m ≥ 2, x0 0, x 0 0, x 0 0,...,xm−2 0 0, x1 αxη . Our results are based on the contraction mapping principle and Krasnoselskii’s fixed point theorem.