On Atangana-Baleanu Nonlocal Boundary Fractional Differential Equations

Abstract

This research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana-Baleanu-type fractional differential equations with Atangana-Baleanu fractional integral conditions. The applied fractional derivatives work as the nonlocal and nonsingular kernel. Upon using Krasnoselskii's and Banach's fixed point techniques, we establish the existence and uniqueness of solutions for proposed problems. Moreover, the Ulam-Hyers stability theory is constructed by using nonlinear analysis. Eventually, we provide two interesting examples to illustrate the effectiveness of our acquired results.