Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

Enes Ata; İ. Onur Kıymaz

doi:10.17776/csj.1005486

EN

Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

Abstract

When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright function. With the help of generalized beta function, new type of generalized Gauss and confluent hypergeometric functions are obtained. Furthermore, some properties of these functions such as integral representations, derivative formulas, Mellin transforms, Laplace transforms and transform formulas are determined. As examples, we obtained the solution of fractional differential equations involving the new generalized beta, Gauss hypergeometric and confluent hypergeometric functions. Finally, we presented their relationship with other generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions, which can be found in the literature.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Enes Ata ^*
0000-0001-6893-8693
Türkiye

İ. Onur Kıymaz
0000-0003-2375-0202
Türkiye

Publication Date

December 27, 2022

Submission Date

October 6, 2021

Acceptance Date

November 30, 2022

Published in Issue

Year 2022 Volume: 43 Number: 4

DOI

https://doi.org/10.17776/csj.1005486

IZ

https://izlik.org/JA29ZY88WB

Cite

RIS / Bibtex

APA

Ata, E., & Kıymaz, İ. O. (2022). Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations. Cumhuriyet Science Journal, 43(4), 684-695. https://doi.org/10.17776/csj.1005486

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Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

Öz

Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations

Abstract

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References

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