Analysis of fractional differential equations with fractional derivative of generalized Mittag-Leffler kernel

Abstract

In this paper, we study classes of linear and nonlinear multi-term fractional differential equations involving a fractional derivative with generalized Mittag-Leffler kernel. Estimates of fractional derivatives at extreme points are first obtained and then implemented to derive new comparison principles for related linear equations. These comparison principles are used to analyze the solutions of the linear multi-term equations, where norm estimates of solutions, uniqueness and several comparison results are established. For the nonlinear problem, we apply the Banach fixed point theorem to establish the existence of a unique solution.