Existence and Hyers-Ulam stability for boundary value problems of multi-term Caputo fractional differential equations

Abstract

The present paper is devoted to discussing a class of nonlinear Caputo-type fractional differential equations with two-point type boundary value conditions. We investigate the existence and uniqueness of the solutions by virtue of the classical Schauder alternative principle and the Banach contraction principle. Furthermore, by means of a novel Gronwall-type inequality, we prove the Hyers-Ulam stability of boundary value problems of multi-term Caputo fractional differential equations. Finally, some numerical examples are given to illustrate the results.