Fractional calculus and applications of family of extended generalized Gauss hypergeometric functions

Mehar Chand; Jyotindra C. Prajapati; Ebenezer Bonyah; Jatinder Kumar Bansal

doi:10.3934/dcdss.2020030

Article Contents

2020, Volume 13, Issue 3: 539-560. Doi: 10.3934/dcdss.2020030

This issue Previous Article Analysis of a Lymphatic filariasis-schistosomiasis coinfection with public health dynamics: Model obtained through Mittag-Leffler function Next Article A novel predictor-corrector scheme for solving variable-order fractional delay differential equations involving operators with Mittag-Leffler kernel

Fractional calculus and applications of family of extended generalized Gauss hypergeometric functions

1.
Department of Mathematics, Baba Farid College, Bathinda-151001, India
2.
Post Graduate Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, India
3.
Department of Mathematics Education, University of Education, Winneba(Kumasi campus), Ghana
4.
Department of Applied Sciences, Guru Kashi University, Bathinda-1513002, India

^* Corresponding author: Jyotindra C. Prajapati
^* Corresponding author: Jyotindra C. Prajapati

Received: June 30, 2018

Revised: August 31, 2018

Published: December 2019

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Abstract

The aim of the present paper is to establish certain new image formulae of family of some extended generalized Gauss hypergeometric functions by applying the operators of fractional derivative involving $ {}_2F_1(.) $ due to Saigo. Furthermore, by employing some integral transforms on the resulting formulas, we obtained some more image formulas and also develop a new and further generalized form of the fractional kinetic equation involving the family of some extended generalized Gauss hypergeometric functions and the manifold generality of the family of functions is discussed in terms of the solution of the fractional kinetic equation. The results obtained here are quite general in nature.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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