Fractional derivative associated with the multivariable I-function,
 the generalized M-series and multivariable polynomials

F.Y.Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V44P530

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 3 | Year 2017 | Article Id. IJMTT-V44P530 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P530

Fractional derivative associated with the multivariable I-function, the generalized M-series and multivariable polynomials

F.Y.Ayant

Abstract

The aim of present paper is to derive a fractional derivative of the multivariable I-function of Prasad [4], associated with a general class of multivariable polynomials defined by Srivastava [9], the Aleph-function of one variable, the generalized M-serie and the generalized Lauricella functions defined by Srivastava and Daoust [10]. We will see the case concerning the multivariable H-function. The results derived here are of a very general nature and hence encompass several cases of interest hittherto scattered in the literature.

Keywords

multivariable I-function, Aleph-function, class of multivariable polynomials, fractional derivative, Lauricella function, binomial expansion, H-function of several variables, M-serie.

References

[1] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, page 208-220
[2] Oldham K.B. and Spanier J The Fractional Calculus Academic Press, New-York (1974).
[3] Pandey N. and Begun R. Fractional integral of product of some special functions. J. Comp. Math. Sci. Vo5(5), 2014 pages 432-439.
[4] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[5] Sharma M. Fractional integration and fractional differentiation of the M-serie. J. Frac. Calc and Appl Anal. Vol 11, No 2 (2008), page 187-191.
[6] Sharma M. Jain R. A note on a generalized series as a special function of fractional calculus. J. Frac. Calc and Appl Anal. Vol 12, No4, page 449-452.
[7] Shekhawat A.S. and Sharma S.K. Fractional derivatives of the Lauricella function and the multivariable I-function along with general class polynomials. Sohaj. J. Math. Vol 3 (3), (2016), page 89-95 .
[8] Shekhawat A.S. and Shaktawat J. Fractional derivatives with the generalized M-series and multivariable polynomials. Int. J. Comp. Eng. Res (IJCER) Vo4 4(2), 2014, page 35-39.
[9] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page 183-191.
[10] Srivastava H.M. and Daoust M.C. Certain generalized Neuman expansions associated with the Kampé de Fériet function. Nederl. Akad. Wetensch. Indag. Math, 31 (1969), page 449-457.
[11] Srivastava H.M. and Panda R. Certains expansion formulae involving the generalized Lauricella functions, II Comment. Math. Univ. St. Paul 24 (1974), page 7-14.
[12] Srivastava H.M. and Panda R. Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24(1975), page.119-137.
[13] Südland N.; Baumann, B. and Nonnenmacher T.F. , Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): page 401-402.

Citation :

F.Y.Ayant, "Fractional derivative associated with the multivariable I-function, the generalized M-series and multivariable polynomials," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 3, pp. 189-196, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P530