Application of a matrix Mittag-Leffler function to the fractional partial integro-differential equation in \(\mathbb{R}^n\)

Volume 33, Issue 4, pp 420--430 https://dx.doi.org/10.22436/jmcs.033.04.08

Publication Date: January 31, 2024 Submission Date: July 11, 2023 Revision Date: December 15, 2023 Accteptance Date: January 04, 2024

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Authors

J. Beaudin - Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba, R7A 6A9, Canada. C. Li - Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba, R7A 6A9, Canada.

Abstract

In this paper, we investigate the uniqueness of solutions to a new fractional partial integro-differential equation (abbreviated FPIDE) with a boundary condition by using a recently established matrix Mittag-Leffler function, Banach's contractive principle, and Babenko's approach. Furthermore, we supply an example that employs the results derived in the paper via a python code which computes an approximate value to the matrix Mittag-Leffler function.

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Keywords

• Banach's contractive principle
• matrix Mittag-Leffler function
• Babenko's approach
• implicit integral equation

MSC

•  35A02
•  35C10
•  35C15
•  26A33

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