Investigation for the
            <i>k</i>
            -analogue of
            <i>τ</i>
            -Gauss hypergeometric matrix functions and associated fractional calculus

Abd-Elmageed, H.; Hidan, Muajebah; Abdalla, Mohamed

doi:10.1080/03081087.2022.2161459

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…On the other hand, recent extensions of special functions build upon the work of esteemed researchers such as Abdalla et al [4,5], Abd-Elmageed et al [6], Hidan et al [7], Fuli He et al [8], and Cuchta et al [9], who have shown a strong interest in studying the extension of special functions in matrix arguments. Contributions to the field by considering various extensions of the gamma, beta, and hypergeometric matrix functions have been documented in [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

Alqarni

2024

Mathematics

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The beta-logarithmic function substantially generalizes the standard beta function, which is widely recognized for its significance in many applications. This article is devoted to the study of a generalization of the classical beta-logarithmic function in a matrix setting called the extended beta-logarithmic matrix function. The proofs of some essential properties of this extension, such as convergence, partial derivative formulas, functional relations, integral representations, inequalities, and finite and infinite sums, are established. Moreover, an application of the extended beta-logarithmic function in matrix arguments is proposed in probability theory. Further, numerical examples and graphical presentations of the new generalization are obtained.

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Section: Introductionmentioning

confidence: 99%

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

Alqarni

2024

Mathematics

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“…We remark in passing that the incomplete extension of the Pochhammer matrix symbol, which was also considered by Bakhet et al [9], has also been used rather widely in the current literature on hypergeometric functions (see, for example, [2], [8], [18] and [19], and references therein). On the other hand, very recently, the authors (see [1,3,11] ) introduced the extensions of the (k; τ )-Gauss hypergeometric matrix function and obtained their various properties. Also, they used these functions to find the solutions of the generalization of fractional kinetic equation.…”

Section: Introductionmentioning

confidence: 99%

On the extended Wright hypergeometric matrix function and its properties

GEZER,

KAANOGLU

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Recently, Bakhet et al. [9] presented the Wright hypergeometric matrix function $_{2}R_{1}^{(\tau )}(A,B;C;z)$ and derived several properties. Abdalla [6] has since applied fractional operators to this function. In this paper, with the help of the generalized Pochhammer matrix symbol $(A;B)_{n}$ and the generalized beta matrix function $\mathcal{B}(P,Q;\mathbb{X})$, we introduce and study an extended form of the Wright hypergeometric matrix function, $_{2}R_{1}^{(\tau )}((A,\mathbb{A}),B;C;z;\mathbb{X}).$ We establish several potentially useful results for this extended form, such as integral representations and fractional derivatives. We also derive some properties of the corresponding incomplete extended Wright hypergeometric matrix function.

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Investigation for the k -analogue of τ -Gauss hypergeometric matrix functions and associated fractional calculus

Cited by 2 publications

References 42 publications

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

On the extended Wright hypergeometric matrix function and its properties

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