Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Abstract

In the present article, we study the solvability of a class of fractional functional integro-differential equations of the CaputoKatugampola type. The existence of solutions is investigated under sufficient conditions as well as the assumptions which guarantee the uniqueness of the solution is explained. Also, we examine the continuous dependence of the solution on the initial condition, the lag function 0 6 ψ(t) 6 t, and the considered nonlinear functional. We give an example to explain our results. The outcomes in this paper extend the results developed by El-Sayed et al. in [A. M. A. El-Sayed, R. G. Ahmed, J. Nonlinear Sci. Appl., 13 (2020), 1–8], recently.