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 c D q x ( 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) = α x ( η ). Our results are based on the contraction mapping principle and Krasnoselskii′s fixed point theorem.