Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

Abstract

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order $\mathrm{\alpha ,\beta }\in (\mathrm{4,5}]$ with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented.