A Matrix Mittag–Leffler Function and the Fractional Nonlinear Partial Integro-Differential Equation in ℝn

Abstract

In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation in Rn with a boundary condition based on Banach’s contractive principle and Babenko’s approach. In addition, we present an example demonstrating applications of the key results derived using a Python code that computes the approximate value of our matrix Mittag–Leffler function.