Existence and data dependence results for fractional differential equations involving atangana-baleanu derivative.

Abstract

In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu fractional derivative. We investigate the fundamental results about the existence, uniqueness, boundedness and dependence of the solution on various data. The analysis is based on a fractional integral operator due to T. R. Prabhakar involving generalized Mittag-Leffler function, the Krasnoselskii’s fixed point theorem and Gronwall-Bellman inequality with continuous functions.