Study on existence and data dependence results for fractional order differential equations

Abstract

In this paper, we examine the multi-derivative nonlinear fractional integro-differential equations involving Atangana-Baleanu fractional derivative of Riemann-Liouville sense. We study the elementary results about the existence and difference solution on different data, based on T. R. Prabhakar fractional integral operator εσ,η,ϑ;c+γ involving generalized Mittag-Leffler function. The results are obtained by using Krasnoselskii's fixed point theorem and Gronwall-Bellman inequality.2010 Subject Classification: 34A60,33E12,34G20.