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

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