Volume 55 | Number 1 | Year 2018 | Article Id. IJMTT-V55P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P501

In this paper, we obtain Nishimoto's N-fractional differintegral of the multivariable Aleph-function and class of multivariable polynomials whose arguments involves the product of two power functions

[1] F.Y. Ayant, An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 31 (3) (2016),142-154.

[2] C. Fox, The G and H-functions as symmetrical Fourier Kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429.

[3] M. Garg and R. Mishra, On r-dimensional N-fractional differintegral of multivariable H-function, J. Indian Acad. Math, 28 (2006), 189-198.

[4] B.P. Gautam and A.S. Asgar, The A-function. Revista Mathematica. Tucuman (1980).

[5] B.P. Gautam and A.S. Asgar, On the multivariable A-function. Vijnana Parishas Anusandhan Patrika,29(4) (1986), 67-81.

[6] K.C. Gupta, S.P. Goyal and R.Garg, N-fractional differintegral of multivariable H-function, Ganita Sandesh, 16 (2002), 5-12.

[7] B.B. Jaimini and K. Nishimoto, N-fractional calculus of generalized Lauricella function of several variables, J. Frac. Calc. 29 (2006), 65-74.

[8] K.S. Kumari, T.M. Vasudevan Nambisan and A.K. Rathie, A study of I-function of two variables, Le Matematiche, 69(1) (2014), 285-305.

[9] A.M. Mathai and R.K. Saxena, The H-function with applications in statistics and other disciplines, John Wiley and Sonc Inc, New York, 1978.

[10] R. Mishra and M. Purohit, N-fractional calculus of H-function of several variables, J. Rajasthan Acad. Phy. Sci. 3(3) (2004), 191-196.

[11] K. Nishimoto, Fractional calculus, Descartes Press, Koriyama, Japan (1984), Vol I ; (1987), Vol II ; (1989), Vol III ; (1991), Vol IV and (1996), Vol V.

[12] Y.N. Prasad, Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 (1986) , 231-237.

[13] Y.N. Prasad and A.K.Singh, Basic properties of the transform involving and H-function of r-variables as kernel, Indian Acad Math, (2) (1982), 109-115.

[14] J. Prathima, V. Nambisan and S.K. Kurumujji, A Study of I-function of Several Complex Variables, International Journalof Engineering Mathematics Vol (2014), 1-12.

[15] A.K. Rathie, A new generalization of generalized hypergeometric functions, LeMatematiche,52(2) (1997), 297 - 310.

[16] R.K. Saxena and K. Nishimoto, N-fractional calculus of the multivariable H-functions, J. Frac. Calc, 31 (2007), 43-52.

[17] V.P. Saxena, Formal solution of certain new pair of dual integral equations involving H-function, Proc. Nat. Acad.Sci. IndiaSect., (2001), A51, 366–375.

[18] K. Sharma, On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences 3(1) ( 2014 ), 1-13.

[19] C.K. Sharma and S.S. Ahmad, On the multivariable I-function. Acta ciencia Indica Math , 20(2) (1994), 113-116.

[20] C.K. Sharma and P.L. Mishra, On the I-function of two variables and its properties. Acta Ciencia Indica Math,17 (1991), 667-672.

[21] H.M. Srivastava, A contour integral involving Fox's H-function. Indian. J. Math, (14) (1972), 1-6.

[22] H.M. Srivastava, A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested byLaguerre polynomial, Pacific. J. Math. 177(1985), 183-191.

[23] H.M.Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24 (1975),119-137.

[24] H.M.Srivastava and R.Panda, Some expansion theorems and generating relations for the H-function of several complex variables II. Comment. Math. Univ. St. Paul. 25 (1976), 167-197.

[25] H.M. Srivastava and N.P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials. Rend. Circ. Mat. Palermo. Vol 32 (No 2) (1983), 157-187.

[26] N. Südland, B. Baumann and T.F. Nonnenmacher, Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998), 401-402.

[27] N.Sudland, B. Baumann and T.F. Nannenmacher, Fractional drift-less Fokker-Planck equation with power law diffusion coefficients, in V.G. Gangha, E.W. Mayr, W.G. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing (CASC Konstanz 2001), Springer, Berlin, 2001, 513–525.

[28] C. Szego, (1975), Orthogonal polynomials. Amer. Math. Soc. Colloq. Publ. 23 fourth edition. Amer. Math. Soc. Providence. Rhodes Island, 1975.

F.Y.Ayant, "N-Fractional Calculus and Multivariable Aleph Function and Generalized Multivariable Polynomials," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 55, no. 1, pp. 1-9, 2018. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V55P501