On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

Zou, Chaojun; Yu, Mimi; Bakhet, Ahmed; He, Fuli

doi:10.1155/2021/5586021

Cited by 7 publications

(1 citation statement)

References 22 publications

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“…In this section, motivated by [21], we introduce the incomplete extended Wright hypergeometric matrix function (IEWHMF) with the help of the incomplete extended beta matrix function defined in (8). Let B, C and X be positive stable matrices in C r×r satisfying the condition (2), and suppose B, C and X commute with each other.…”

Section: Incomplete Extended Wright Hypergeometric Matrix Functionmentioning

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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Section: Incomplete Extended Wright Hypergeometric Matrix Functionmentioning

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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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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The incomplete matrix beta function and its application to first Appell hypergeometric matrix function

Bakhet

et al. 2023

Linear and Multilinear Algebra

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On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

Cited by 7 publications

References 22 publications

On the extended Wright hypergeometric matrix function and its properties

On the extended Wright hypergeometric matrix function and its properties

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

The incomplete matrix beta function and its application to first Appell hypergeometric matrix function

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