An Introductory Overview of Fractional-Calculus Operators Based Upon the Fox-Wright and Related Higher Transcendental Functions

Abstract

This survey-cum-expository review article is motivated essentially by the widespread usages of the operators of fractional calculus (that is, fractional-order integrals and fractional-order derivatives) in the modeling and analysis of a remarkably large variety of applied scientific and real-world problems in mathematical, physical, biological, engineering and statistical sciences, and in other scientific disciplines. Here, in this article, we present a brief introductory overview of the theory and applications of the fractional-calculus operators which are based upon the general Fox-Wright function and its such specialized forms as (for example) the widely- and extensively investigated and potentially useful Mittag-Leffter type functions.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.