Generalized Fractional Calculus Operators
Involving Multivariable Aleph Function

Akanksha Shukla; Shalini Shekhawat; Kanak Modi

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P516

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P516

Generalized Fractional Calculus Operators Involving Multivariable Aleph Function

Akanksha Shukla, Shalini Shekhawat, Kanak Modi

Citation :

Akanksha Shukla, Shalini Shekhawat, Kanak Modi, "Generalized Fractional Calculus Operators Involving Multivariable Aleph Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 132-138, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P516

Abstract

This paper involves the brief study of generalized fractional calculus and multivariable Aleph function. In this paper we presented three theorems consisting multivariable Aleph function and generalized fractional calculus operator. The Aleph function used in theorems is general by nature and can be reduced into many other functions.

Keywords

Fractional Calculus, Multivariable Aleph Function, Fractional Calculus operator

References

[1] C.K. Sharma, S.S.Ahmad. On the multivariable I-function. Acta ciencia Indica Math, 20(2): 113-116,1994.
[2] D. Kumar, S. Kumar.Fractional integrals and derivatives of the generalized Mittag-Leffler type function. International Scholarly Research Notices, Article ID 907432, 2014.
[3] D.Kumar, R.K. Gupta, D. S.Rawat , J. Daiya. Hypergeometric fractional integrals of multiparameter K-Mittag-Leffler function. Nonlinear Sci Lett A, 9(1): 17-26, 2018.
[4] F.Y. Ayant.An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT), 3 (3):142-154, 2016.
[5] F.Y. Ayant., Fourier Bessel Expansion for Aleph-Function of several variables II. Journal of Ramanujan Society of Mathematics and Mathematical Sciences,5(1): 39- 46, 2016.
[6] F.Y. Ayant., Certains classes generating functions associated with the Aleph-function of several variables II. South East Asian Journal of Mathematics and Mathematical Sciences, Accepted for Publication in 2018.
[7] H.M. Srivastava, R.Panda. Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24:119-137, 1975.
[8] K. Sharma., On the integral representation and applications of the generalized function of two Variables. International Journal of Mathematical Engineering and Sciences, 3(1):1-13, 2014.
[9] M. Saigo., A remark on integral operators involving the Gauss hypergeometric functions. Math. Rep., College General Ed. Kyushu Univ., 11:135-143,1978.
[10] N.Sudland, B. Baumann, T.F. Nonnenmacher, Open problem: who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4): 401-402, 1998.
[11] R.K. Saxena, M. Saigo., Certain properties of Fractional Calculus operator associated with generalized Mittag-Leffler function. Frac. Cal. Appl. Anal., 8(2): 141-154, 2005.
[12] R.K. Gupta, B.S. Shaktawat, D. Kumar, Certain relation of generalized fractional calculus associated with the generalized Mittag-Leffler function. Journal of Rajasthan Academy of Physical Sciences, 15(3):117-126,2016.
[13] S.G. Samko, A.A. Kilbas, O.I. Marichev.Fractional Integral and Derivatives, Theory and Applications. Gordon and Breach, Yverdon et alibi, (1993).
[14] V.B.L. Chaurasia, S. C. Pandey, On the fractional calculus of generalized Mittag-Leffler Function. Math. Sci., 20:113- 122,2010.