On the q-Hypergeometric Matrix Function rφs(A, B; Ci; Dj; q; z) and Its q-Fractional Calculus

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Authors

  • Ravi Dwivedi
     Department of Mathematics, Swami Atmanand Government English Medium Model College, Jagdalpur(CG), 494001 ,IN
  • Reshma Sanjhira
     Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Tech., Changa-388 421, Dist: Anand ,IN

DOI:

https://doi.org/10.18311/jims/2024/36132

Keywords:

Basic hypergeometric function, Mittag-Leffer function, Matrix functional calculus.

Abstract

In this paper, we introduce a q-hypergeometric matrix function rφs(A, B; Ci; Dj; q; z) and investigate their regions of convergence. We determine some q-matrix contiguous function relations, a q-integral representation and q-difference formulas satisfied by rφs(A, B; Ci; Dj; q; z) Certain properties of this matrix function have also been studied from q-fractional calculus point of view. Finally, we emphasize on the special cases of rφs(A, B; Ci; Dj; q; z).

 

 

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Published

2024-01-01

How to Cite

Dwivedi, R., & Sanjhira, R. (2024). On the q-Hypergeometric Matrix Function <sub>r</sub>φ<sub>s</sub>(A, B; C<sub>i</sub>; D<sub>j</sub>; q; z) and Its q-Fractional Calculus. The Journal of the Indian Mathematical Society, 91(1-2), 11–24. https://doi.org/10.18311/jims/2024/36132

Issue

Volume 91, Issue 1-2, January-June 2024

Section

Articles

License

Copyright (c) 2024 Ravi Dwivedi, Reshma Sanjhira

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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References

R. P. Agarwal, Certain fractional q-integrals and q-derivatives, Mathematical Proceedings of the Cambridge Philosophical Society, 66 (1969), 365–370.

A. G. Constantine and R. J.Muirhead, Partial differential equations for hypergeometric functions of two argument matrices, J. Multivariate Anal., 2 (1972), 332–338.

R. Dwivedi and V. Sahai, On the basic hypergeometric matrix functions of two variables, Linear Multilinear Algebra, 67(1) (2019), 1–19.

G. Gasper and M. Rahman, Basic hypergeometric series, Second edition. Encyclopedia of Mathematics and its Applications, 96. Cambridge University Press, Cambridge, 2004.

G.H. Golub and C. F.Van Loan, Matrix Computation, The Johns Hopkins Univ. Press, Baltimore, MA, 1989.

R. Gorenflo, A. A. Kilbas, F. Mainardi and S. V. Rogosin, Mittag-Leffler functions, related topics and applications, Springer Monographs in Mathematics. Springer, Heidelberg, 2014. xiv+443 pp.

G. Mittag-Leffler, Sur la nouvelle fonction Eα(x), C. R. Acad. Sci., Paris, 137 (1903), 554-558.

T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7–15.

M.G. Bin-Saad and M. A.Pathan, On pseudo Laguerre matrix polynomials, operational identities and qusi-monomiality, Advances in Linear Algebra and Matrix Theory, 8(2) (2018), 87–95.

T. O. Salim, Some properties relating to the generalized Mittag-Leffler function, Adv. Appl. Math. Anal., 4 (1) (2009), 21–30.

R. Sanjhira, B. V. Nathwani and B. I. Dave, Generalized Mittag-Leffler matrix function and associated matrix polynomials, J. Indian Math. Soc. (N.S.), 86 (1-2)(2019), 161–178.

A. Salem, On a q-gamma and a q-beta matrix functions, Linear Multilinear Algebra, 60 (6) (2012),683–696.

A. Salem,The basic Gauss hypergeometric matrix function and its matrix q-difference equation, Linear Multilinear Algebra, 62 (3) (2014), 347–361.

M. Sharma and R. Jain, A note on a generalized M-series as a special function of fractional calculus, Frac. Calc. Appl. Anal., 12 (4) (2009), 449–452.

W. F.Trench, Invertibly convergent infinite products of matrices, with applications to difference equations, Comput. Math. Appl., 30 (11) (1995), 39–46.