A qualitative study on generalized Caputo fractional integro-differential equations

Abstract The aim of this article is to discuss the uniqueness and Ulam–Hyers stability solutions for a nonlinear fractional integro-differential equation involving generalized Caputo operator. used operator generated by iterating local integral form $(I_{a}^{\rho }f)(t)=\int _{a}^{t}f(s)s^{\rho -1}\,ds$ ( I a ρ f ) t = ∫ s − 1 d . Our reported results are obtained in Banach space absolutely continuous functions that rely on Babenko’s technique Banach’s fixed point theorem. Besides, our main findings illustrated some examples.