New frame of fractional neutral ABC-derivative with IBC and mixed delay

In this manuscript, we describe fractional differential equations with neutral, integral boundary conditions and mixed delay using Atangana-Baleanu derivatives, which include the generalized Mittag-Leffler kernel. We determine the existence and uniqueness of results and analysis by fixed point method. Moreover, we explained the stability of the fractional differential equation in the frame of Ulam-Hyers. Then, we investigate an example with various values and illustrate the outcomes graphically.

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In this manuscript, we describe the method of using Atangana-Baleanu derivatives to describe fractional differential equations, and determine the existence and uniqueness of their solutions through fixed point method. We also discuss the stability of fractional differential equations and illustrate the results graphically with an example.