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

The present paper is devoted to discussing a class of nonlinear Caputo-type fractional integro-differential equations with two-point type boundary value conditions. We investigate the existence and uniqueness of the solutions by virtue of the classical Leray-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.