Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 5, Issue 1


Published
on

March 31, 2020


Pages

369-384


DOI

Article

Fractional Calculus of the Extended Hypergeometric Function

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Authors

Recep Şahin Affiliation:
Department of Mathematics, Kırıkkale University, Faculty of Science Kırıkkale, Turkey
and Oğuz Yağcı Affiliation:
Department of Mathematics, Kırıkkale University, Faculty of Science Kırıkkale, Turkey


Abstract

Here, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators. Furthermore, by applying certain integral transforms on the resulting formulas and develop a new futher generalized form of the fractional kinetic equation involving the generalized Gauss hypergeometric function. Also, we obtain generating functions for generalization of extended hypergeometric function..


Keywords

Gamma function, beta function, hypergeometric functions, extended hypergeometric function, integral transforms, fractional calculus operators, generating functions, Primary 33C15, 33C20, 33C60, 33D70, Secondary 26A33, 33C65, 33C90


Citation

Şahin, R. & Yağcı, O. (2020). Fractional calculus of the extended hypergeometric function. Applied Mathematics and Nonlinear Sciences, 5(1), 369–384. https://doi.org/10.2478/amns.2020.1.00035

Published by: Engineering Journals

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