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.

12 pages

References in corpus (4)

• A Caputo fractional derivative of a function with respect to another function
• On some new properties of fractional derivatives with Mittag-Leffler kernel
• The Prabhakar or three parameter Mittag--Leffler function: theory and application
• General fractional calculus and Prabhakar's theory