Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions

Agarwal, Praveen; Rassias, Themistocles M.; Singh, Gurinder; Jain, Shilpi

doi:10.1007/978-3-030-31339-5_8

Cited by 4 publications

(2 citation statements)

References 54 publications

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“…Several researchers have explored the features of integral transforms and special functions in many different aspects [Agarwal, Praveen(2012), Khan,et al (2016), Gradshteyn, I. S., and I. M. Ryzhik(1994), Li, Chun-Fang(2007)]. Multivariable special functions naturally appear in a variety of mathematical and practical situations.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Integral Transformation Associated with Extended Generalized Srivastava’s Hypergeometric Multi Variable Special Function

Kulmitra,

Tiwari

2024

Mikailalsys. J. of. Adv. Eng. Int.

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In recent year study on multivariate special functions and Integral transformation have been booming. In this work, we have focused on Srivastava hypergeometric function , , and with triple variable. We have discussed the literature study and motivation from the recent works on the extension of Srivastava’s multivariable hypergeometric function , , and . In this paper, the extension of , , and is studied based on the generalized beta function and the generalized Pochhammer’s symbol . Furthermore, the Mellin integral transformation and Inverse Mellin integral transformation have been studied for the based extension of the functions , , and . A few of the most recent uses of these transformations in various scientific and engineering fields are also highlighted in this paper. In general, this work seeks to offer a thorough overview of recent breakthroughs in the importance and applications of several integral transforms of Multivariable functions.

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Section: Introductionmentioning

confidence: 99%

Investigation of Integral Transformation Associated with Extended Generalized Srivastava’s Hypergeometric Multi Variable Special Function

Kulmitra,

Tiwari

2024

Mikailalsys. J. of. Adv. Eng. Int.

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“…e gamma, digamma, and polygamma functions have an increasing and recognized role in fractional differential equations, mathematical physics, the theory of special functions, statistics, probability theory, and the theory of infinite series. e reader may refer, for example, to [1][2][3][4][5][6][7][8][9]. ese functions are directly connected with a variety of special functions such as zeta function, Clausen's function, and hypergeometric functions.…”

Section: Introductionmentioning

confidence: 99%

Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

Bakhet

Akel

et al. 2020

Mathematical Problems in Engineering

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In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.

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On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus

Qadha,

Bakhet

2024

Math Methods in App Sciences

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In this paper, our aim is to introduce a new definition of ( ‐incomplete Wright hypergeometric matrix functions ( ‐IWHMFs) using the ‐incomplete Pochhammer matrix symbol. First, we define the ‐incomplete gamma matrix function and introduce the ‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these ‐IWHMFs. We have also obtained some results regarding the ‐fractional calculus operators of these ‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the ‐IWHMFs.

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Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions

Cited by 4 publications

References 54 publications

Investigation of Integral Transformation Associated with Extended Generalized Srivastava’s Hypergeometric Multi Variable Special Function

Investigation of Integral Transformation Associated with Extended Generalized Srivastava’s Hypergeometric Multi Variable Special Function

Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus

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