Existence Solutions of ABC-Fractional Differential Equations with Periodic and Integral Boundary Conditions

The nonlinear fractional differential equation (FDE) is discussed in this study. First, we will investigate the existence and uniqueness solution of the nonlinear differential equation to the Atangana-Baleanu fractional derivative in the sense of Caputo with the initial periodic condition and integral boundary condition by Krasnoselskii’s and Banach fixed point theorems. Then, we will study the Hyers-Ulam stability of our problem. Finally, we presented an example to demonstrate the use of our main theorems.