Existence results for a coupled system of nonlinear multi‐term fractional differential equations with anti‐periodic type coupled nonlocal boundary conditions

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of nonlinear multi‐term fractional differential equations with anti‐periodic type coupled nonlocal boundary conditions. The existence of a unique solution is proved via Banach contraction mapping principle, while two existence results are proved by using Krasnosel'skiic̆'s fixed point theorem and Leray‐Schauder alternative. We also discuss a variant of the proposed problem involving fractional differential types nonlinearities. The obtained results are well illustrated by numerical examples.