Solutions and Anti-Periodic Solutions for Non-Local Impulsive Differential Equations and Inclusions Containing the Weighted Generalized Atangana–Baleanu Fractional Derivative in Banach Spaces

This paper examines the sufficient conditions that guarantee the existence of solutions and anti-periodic solutions to five classes of fractional differential equations and inclusions involving the weighted generalized Atangana–Baleanu differential operator of order δ∈(1,2) under non-local conditions and with instantaneous or non-instantaneous impulses in Banach spaces whose dimension is infinite. First, we deduce some novel properties of this differential operator, then derive the formula for the solutions and anti-periodic solutions, and investigate their existence for the problems presented. Our method relies on certain properties of the Atangana–Baleanu differential operator, which we will obtain, as well as the fixed-point theorems that can be applied to the functions and multi-valued functions. Our work generalizes recently published results. In the final section, we present some examples to illustrate how our theoretical results can be applied.