A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
Classical Analysis and ODEs
2021-05-03 v1
Abstract
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral operator which has many interesting properties. The motivation for these definitions is twofold: firstly their link with some fundamental fractional differential equations involving two independent fractional orders, and secondly the fact that they emerge naturally from certain applications in bioengineering.
Cite
@article{arxiv.2002.12171,
title = {A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators},
author = {Arran Fernandez and Cemaliye Kürt and Mehmet Ali Özarslan},
journal= {arXiv preprint arXiv:2002.12171},
year = {2021}
}