On a $$\psi $$-Generalized Fractional Derivative Operator of Riemann–Liouville with Some Applications

Singhal, Meenakshi; Mittal, Ekta

doi:10.1007/s40819-020-00892-5

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Some properties of these generalized beta are investigated, Kumar confluent, Appell's and Lauricella's hypergeometric functions, most of which are analogous with the classical and other related generalized beta functions. These generalized functions can be used to study theory of fractional integral and differential calculus (see for example, Pucheta, 2017;Rahman et al, 2018;Shadab et al, 2018;Nisar et al, 2019;Singhal and Mittal, 2020) and in the provision of the extended special function such as Mittag-Leffler, Bessel-Maitland and Wright (refer to, Khan et al, 2020a, b).…”

Section: Discussionmentioning

confidence: 99%

On a New Generalized Beta Function Defined by the Generalized Wright Function and Its Applications

Abubakar¹,

Patel²

2021

MJoC

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Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some of its properties such as symmetric properties, summation formulas, integral representations, connection with some other special functions such as classical beta, error, Mittag – Leffler, incomplete gamma, hypergeometric, classical Wright, Fox – Wright, Fox H and Meijer G – functions. Furthermore, the generalized beta function is used to generalize classical and other extended Gauss hypergeometric, confluent hypergeometric, Appell’s and Lauricella’s functions.

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Section: Discussionmentioning

confidence: 99%

On a New Generalized Beta Function Defined by the Generalized Wright Function and Its Applications

Abubakar¹,

Patel²

2021

MJoC

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“…This generalized extended Wright function can be used to study generalized special functions (refer to, [1], [2], [4] and [13]]) and fractional integral and differential calculus such as Riemann-Liouville and Caputo fractional derivative and integral (see for example, [18]).…”

Section: Discussionmentioning

confidence: 99%

On the Generalized Extended Wright Function

Abubakar¹,

Dudi²

2021

IJFMA

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The main object of this paper is to introduce a new generalized extended Wright function, for the new generalized extended Wright function properties such as integral representations, Euler’s beta, Mellin, inverse Mellin, Jacobi, Gegenbaur, and Legendre transforms are proposed and investigated. Moreover, some derivative formulas, classical and extended Riemann-Liouville fractional derivative and integral are also proposed.

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Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions

Verma,

Yadav,

Sharan

et al. 2024

Analysis

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In this paper, we investigate the matrix analogues of the Ψ-beta and Ψ-gamma functions, as well as their properties. With the help of the Ψ-beta matrix function (BMF), we introduce the Ψ-Gauss hypergeometric matrix function (GHMF) and the Ψ-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the Ψ-Appell and the Ψ-Lauricella matrix functions are defined by applications of the Ψ-BMF, and their integral representations are also given.

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On a $$\psi $$-Generalized Fractional Derivative Operator of Riemann–Liouville with Some Applications

Cited by 3 publications

References 14 publications

On a New Generalized Beta Function Defined by the Generalized Wright Function and Its Applications

On a New Generalized Beta Function Defined by the Generalized Wright Function and Its Applications

On the Generalized Extended Wright Function

Some properties of Ψ-gamma, Ψ-beta and Ψ-hypergeometric matrix functions

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