Some Applications of Banach Fixed Point and Leray Schauder Theorems for Fractional Boundary Value Problems

Abstract

In this paper, we study a boundary value problem of nonlinear fractional differential equations of order α, 3 < α < 4. We use Banach fixed point theorem to establish new results on the existence and uniqueness of solutions. Then, we use Leray-Schauder nonlinear alternative to prove some existence results.