<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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..</p></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..

Fractional Calculus of the Extended Hypergeometric Function

Kırıkkale University, Faculty of Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Fractional Calculus of the Extended Hypergeometric Function"}

Here, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators....

Fractional Calculus of the Extended Hypergeometric Function

Published Online: Mar 31, 2020

Page range: 369 - 384

Received: Jun 14, 2019

Accepted: Jun 26, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00035

Keywords
Gamma function, beta function, hypergeometric functions, extended hypergeometric function, integral transforms, fractional calculus operators, generating functions

© 2020 Recep Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fractional Calculus of the Extended Hypergeometric Function

Published Online: Mar 31, 2020

Page range: 369 - 384

Received: Jun 14, 2019

Accepted: Jun 26, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00035

KeywordsGamma function, beta function, hypergeometric functions, extended hypergeometric function, integral transforms, fractional calculus operators, generating functions

© 2020 Recep Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Gamma function, beta function, hypergeometric functions, extended hypergeometric function, integral transforms, fractional calculus operators, generating functions