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.

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