A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations

Enes Ata; Kıymaz Onur Kıymaz; Praveen Agarwal; Shilpi Jain

doi:10.1016/B978-0-44-315423-2.00012-6

A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations

Enes Ata
, Kıymaz Onur Kıymaz
, Praveen Agarwal
, Shilpi Jain

Nonlinear Dynamic Research Centre (NDRC)

Kırşehir Ahi Evran University
International College of Engineering
Poornima College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

5 Scopus citations

Abstract

In this paper, we have defined generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions with the help of generalized M-series. Furthermore, we have obtained some properties of these functions, such as integral representations, summation formulas, and derivative formulas. Then we applied beta, Mellin, Laplace, Sumudu, Elzaki, and general integral transformations to new generalized special functions and obtained solutions of fractional differential equations containing new generalized special functions. Finally, we presented the relationship between generalized special functions in the literature and new generalized special functions.

Original language	English
Title of host publication	Fractional Differential Equations
Subtitle of host publication	Theoretical Aspects and Applications
Publisher	Elsevier
Pages	95-114
Number of pages	20
ISBN (Electronic)	9780443154232
ISBN (Print)	9780443154249
DOIs	https://doi.org/10.1016/B978-0-44-315423-2.00012-6
State	Published - 1 Jan 2024

Keywords

Beta function
Confluent hypergeometric function
Fractional differential equations
Gamma function
Gauss hypergeometric function
Integral transforms

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10.1016/B978-0-44-315423-2.00012-6

Cite this

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keywords = "Beta function, Confluent hypergeometric function, Fractional differential equations, Gamma function, Gauss hypergeometric function, Integral transforms",

author = "Enes Ata and \{Onur Kıymaz\}, Kıymaz and Praveen Agarwal and Shilpi Jain",

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A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations. / Ata, Enes; Onur Kıymaz, Kıymaz; Agarwal, Praveen et al.
Fractional Differential Equations: Theoretical Aspects and Applications. Elsevier, 2024. p. 95-114.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations

AU - Ata, Enes

AU - Onur Kıymaz, Kıymaz

AU - Agarwal, Praveen

AU - Jain, Shilpi

PY - 2024/1/1

Y1 - 2024/1/1

N2 - In this paper, we have defined generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions with the help of generalized M-series. Furthermore, we have obtained some properties of these functions, such as integral representations, summation formulas, and derivative formulas. Then we applied beta, Mellin, Laplace, Sumudu, Elzaki, and general integral transformations to new generalized special functions and obtained solutions of fractional differential equations containing new generalized special functions. Finally, we presented the relationship between generalized special functions in the literature and new generalized special functions.

AB - In this paper, we have defined generalized gamma, beta, Gauss hypergeometric and confluent hypergeometric functions with the help of generalized M-series. Furthermore, we have obtained some properties of these functions, such as integral representations, summation formulas, and derivative formulas. Then we applied beta, Mellin, Laplace, Sumudu, Elzaki, and general integral transformations to new generalized special functions and obtained solutions of fractional differential equations containing new generalized special functions. Finally, we presented the relationship between generalized special functions in the literature and new generalized special functions.

KW - Beta function

KW - Confluent hypergeometric function

KW - Fractional differential equations

KW - Gamma function

KW - Gauss hypergeometric function

KW - Integral transforms

UR - https://www.scopus.com/pages/publications/85199074848

U2 - 10.1016/B978-0-44-315423-2.00012-6

DO - 10.1016/B978-0-44-315423-2.00012-6

M3 - Chapter

AN - SCOPUS:85199074848

SN - 9780443154249

SP - 95

EP - 114

BT - Fractional Differential Equations

PB - Elsevier

ER -

A study on the properties of new generalized special functions, their integral transformations, and applications to fractional differential equations

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Keywords

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