A natural extension of Mittag-Leffler function associated with a triple infinite series
Abstract
We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by putting to use of the eminent Hankel's integral. We also investigate Laplace integral relation and convolution result for a univariate version of this function. Moreover, we present fractional derivative of trivariate Mittag-Leffler function in Caputo type and we also discuss Riemann- Liouville type fractional integral and derivative of this function. The link of trivariate Mittag-Leffler function with fractional differential equation systems involving different fractional orders is necessary on certain applications in physics. Thus, we provide an exact analytic solutions of homogeneous and inhomogeneous multi-term fractional differential equations by means of a newly defined trivariate Mittag-Leffler functions.
Keywords
Cite
@article{arxiv.2011.03999,
title = {A natural extension of Mittag-Leffler function associated with a triple infinite series},
author = {Ismail T. Huseynov and Arzu Ahmadovay and Gbenga O. Ojo and Nazim I. Mahmudov},
journal= {arXiv preprint arXiv:2011.03999},
year = {2020}
}