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arXiv · 2210.12354

On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties

Ravi Dwivedi·Reshma Sanjhira
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Abstract

The main objective of the present paper is to introduce and study the function $_pR_q(A, B; z)$ with matrix parameters and investigate the convergence of this matrix function. The contiguous matrix function relations, differential formulas and the integral representation for the matrix function $_pR_q(A, B; z)$ are derived. Certain properties of the matrix function $_pR_q(A, B; z)$ have also been studied from fractional calculus point of view. Finally, we emphasize on the special cases namely the generalized matrix $M$-series, the Mittag-Leffler matrix function and its generalizations and some matrix polynomials.

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Ravi Dwivedi, Reshma Sanjhira. 2022-10-22. On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties. https://doi.org/10.46298/cm.10205

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