Existence and stability analysis to nonlocal implicit problems with ψ-piecewise fractional operators

Abstract

In this work, we investigate the existence, uniqueness, and Ulam-Hyers stability results for classes of nonlocal implicit problems involving ψ-piecewise Caputo fractional operators. Our approach is depends on fixed point theorems of Banach and Schaefer. Furthermore, the ensuring of the existence of solutions is shown by Ulam-Hyer's stability. At last, an example is given to show and approve our results.