EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \kappa $-CAPUTO DERIVATIVE

This paper is concerned with a class of nonlinear fractional differential equations with two-term $ \kappa $-Caputo fractional derivatives. The existence and uniqueness results are obtained for boundary value problems by using the Banach fixed point theorem and Leray-Schauder nonlinear alternative. The Hyers-Ulam stability is also considered. Some examples are discussed to illustrate the obtained results.