Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function *

Abstract

Introducing the new generalized multivariate Mittag-Leffler function, we consider the uniqueness of solutions to a boundary value problem of the fractional nonlinear partial integro-differential equation using Banach’s fixed point theorem and Babenko’s technique. In addition, we use Python which is a high-level language efficiently dealing with the summation of multi indices to compute the approximate value of the generalized Mittag-Leffler function, and provide an example showing applications of key results derived. Mathematics Subject Classification: 65M25, 65Q30, 35C10, 35C15, 26A33