Properties of fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function

Abstract

This paper aims to investigate properties associated with fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function. We prove that the Cauchy problem and the Volterra integral equation are equivalent. We find a closed-form to the solution of the Cauchy problem using successive approximations method and $\psi$-Caputo fractional derivative.