IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENTS AND THE CONVEX COMBINED CAPUTO DERIVATIVE

Abstract

We prove the existence and uniqueness results for a class of implicit fractional differential equations involving the combined Caputo fractional derivative with advanced arguments by using the fixed point theorems of Banach and nonlinear alternative of Leray and Schauder. We will also establish the Ulam stability and give some examples to show the applicability of our results.