Existence and Uniqueness Results for Integro Fractional Differential Equations with Atangana-Baleanu Fractional Derivative

Abstract

In this article, we present the existence and uniqueness(EU) results for fractional differential equations(FDEs) with a new direction in Atangana-Baleanu-Caputo (ABC) fractional derivative approach.  The studied problem is considered with non-local integral initial condition.  The existence of solution is investigated by the implementation of Krasnoselskii's fixed point theorem for proposed equations. The uniqueness of the result is derived with the help of the Banach contraction mapping principle. In the end, an example is presented to smooth the understanding of the derived results.