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On a solution of a fractional hyper-Bessel differential equation by means of a multi-index special function

  • Riccardo Droghei
Published/Copyright: October 28, 2021

Abstract

In this paper we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for a case of hyper-Bessel operator involving Caputo fractional derivatives. We show that by giving particular values to the parameters involved in this special function, this leads to some known special functions (as the classical Wright function, the α-Mittag-Leffler function, the Tricomi function, etc.) that on their turn appear as cases of the so-called multi-index Mittag-Leffler functions. As an application, we mention that this new generalization Wright function nis an isochronous solution of a nonlinear fractional partial differential equation.

Acknowledgements

The author is grateful to Dr. Roberto Garra for providing essential information, to the Editor who helped to enter this topic in deep, and to expand the bibliography.

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Received: 2021-02-21
Revised: 2021-08-05
Published Online: 2021-10-28
Published in Print: 2021-10-26

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