Analysis of nonlinear implicit fractional differential equations with the Atangana-Baleanu derivative via measure of non-compactness

In this study, we proved existence results for nonlinear implicit fractional differential equations with the Caputo version of the Atangana-Baleanu derivative, subject to the boundary and nonlocal initial conditions. The Kuratowski’s measure of non-compactness and its associated fixed point theorems–Darbo’s fixed point theorem and Mönchh’s fixed point theorem, are the foundation for the analysis in this paper. We support our results with examples of nonlinear implicit fractional differential equations involving the Caputo version of the Atangana-Baleanu derivative subject to both boundary and nonlocal initial conditions. In addition, we provide solutions to the problems we considered.