Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

An Extended Version of the r+1Rs;k(B;C; z) Matrix Function

Version 1 : Received: 28 December 2023 / Approved: 28 December 2023 / Online: 28 December 2023 (15:17:30 CET)

How to cite: Shehata, A. An Extended Version of the r+1Rs;k(B;C; z) Matrix Function. Preprints 2023, 2023122191. https://doi.org/10.20944/preprints202312.2191.v1 Shehata, A. An Extended Version of the r+1Rs;k(B;C; z) Matrix Function. Preprints 2023, 2023122191. https://doi.org/10.20944/preprints202312.2191.v1

Abstract

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, di erential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

Keywords

r+1Rs,k(B, C, z) matrix function; k-fractional integral operators; k-fractional derivative operators; Riemann-Liouville k-fractional integral; k-Gamma matrix function; k-Beta matrix function

Subject

Physical Sciences, Mathematical Physics

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