Some integral properties in the theory of generalized $k-$Bessel matrix functions
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Abstract
The main purpose of this article is to define some original properties in the theory of the generalized modified $k-$Bessel matrix functions. These special functions, defined in terms of Wright matrix functions, are generalized and their properties studied in depth. Moreover, it is shown their application to the analysis of certain generalized integral formulas involving the generalized modified $k-$Bessel matrix function.
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References
[1] M. Ali, W. A. Khan and I. A. Khan, On certain integral transform involving generalized Bessel-Maitland function with applications, Journal of Fractional Calculus and Applications, 11(1) (2020), 82–90.
[2] R. Diaz and E. Pariguan, On hypergeometric functions and k-Pochhammer symbol, Divulgaciones Matemáticas, 15(2) (2007), 179–192.
[3] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience Publishers, New York, (1957).
[4] M. Ghayasuddin and W. A. Khan, A new extension of Bessel Maitland function and its properties, atematicki Vesnik, (2018), 1–11.
[5] L. Jódar and J. C. Cortés, Some properties of Gamma and Beta matrix functions, Applied Mathematics Letters, 11 (1998), 89–93.
[6] L. Jódar and J. C. Cortés, On the hypergeometric matrix function, Journal of Computational and Applied Mathematics, 99 (1998), 205–217.
[7] W. A. Khan and K. S. Nisar, Beta type integral formula associated with Wright generalized Bessel function, Acta Mathematica Universitatis Comenianae, 87(1) (2018), 117–125.
[8] T. M. MacRobert, Beta functions formulae and integrals involving E-function, Mathematische Annalen, 142 (1961), 450–452.
[9] S. R. Mondal and K. S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Communications of the Korean Mathematical Society, 32 (2017), 47–53.
[10] S. Mubeen, M. Naz and G. Rahman, A note on k-hypergeometric differential equations, Journal of Inequalities and Special Functions, 4(3) (2013), 38–43.
[11] S. Mubeen, G. Rahman and M. Arshad, k-Gamma, k-Beta matrices and their properties, Journal of Mathematics and Computer Science, 5 (2015), 647–657.
[12] K. S. Nisar, On the generalized modified k-Bessel function of first kind, Communications of the Korean Mathematical Society, 32(4) (2017), 909–914. [13] K. S. Nisar, W. A. Khan and A. H. Abusufian, Certain integral transforms of k-Bessel function, Palestine Journal of Mathematics, 7(1) (2018), 161–166.
[14] F. Oberhettinger, Tables of Mellin Transforms, Springer, New York, (1974).
[15] L. G. Romero, G. A. Dorrego and R. A. Cerutti, The k-Bessel function of first kind, International Mathematical Forum, 7(38) (2012), 1859–1864.
[16] A. Shehata, Extended Bessel matrix functions, Mathematical Sciences and Applications E-Notes, 6(1) (2018), 1–11.
[17] A. Shehata, Some properties associated with the Bessel matrix functions, Konuralp Journal of Mathematics, 5(2) (2017), 24–35.
[18] A. Shehata, Some relations on the generalized Bessel matrix polynomials, Asian Journal of Mathematics and Computer Research, 17(1) (2017), 1–25.
[19] A. Shehata, A new extension of Bessel matrix functions, Southeast Asian Bulletin of Mathematics, 40(2) (2016), 265–288.
[20] A. Shehata and S. Khan, On Bessel-Maitland matrix function, Journal Mathematica (Cluj), 57(80)(1-2) (2015), 90–103.
[21] D. L. Suthar, A. M. Khan, A. Alaria, S. D. Purohit and J. Singh, Extended BesselMaitland function and its properties pertaining to integral transforms and fractional calculus, AIMS Mathematics, 5(2) (2020), 1400–1410.