Mohamed I. Abbas

Nonlinear Atangana-Baleanu Fractional Differential Equations Involving the Mittag-Leffler Integral Operator

abstract:
This paper intends to investigate the existence and uniqueness of solutions for some nonlinear Atangana-Baleanu fractional differential equations involving the Mittag-Leffler integral operator. By means of Schauder's fixed point theorem and Banach's fixed point theorem, the existence and uniqueness results are obtained. A generalized fractional order free electron laser equation is given as an application.

Mathematics Subject Classification: 34A08, 33E12, 47G10

Key words and phrases: Atangana-Baleanu fractional derivative, Schauder's fixed point theorem, Mittag-Leffler operator