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Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions

1
Environment, Health and Safety, IMEC, 3001 Leuven, Belgium
2
Neuroscience Research Flanders, 3001 Leuven, Belgium
Fractal Fract 2019, 3(1), 4; https://doi.org/10.3390/fractalfract3010004
Received: 23 December 2018 / Revised: 22 January 2019 / Accepted: 22 January 2019 / Published: 25 January 2019
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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Abstract

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized Erdélyi-Kober fractional differential and integral operators is demonstrated and discussed. View Full-Text
Keywords: Wright function; Gamma function; Beta function; fractional calculus; Erdélyi-Kober operators Wright function; Gamma function; Beta function; fractional calculus; Erdélyi-Kober operators
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Prodanov, D. Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions. Fractal Fract 2019, 3, 4.

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