Volume 50 | Number 2 | Year 2017 | Article Id. IJMTT-V50P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P512
In this paper, our objective is to investigate the basic analogue of a new hypergeometric function, which is a generalization of the basic I-function. In this regard, the application of Kober type q-integral operator with new hypergeometric function has been discussed. Similar result obtained by other authors follows as special cases of our findings.
[1] Agarwal, R.P. Certain fractional q-integrals and qderivatives, Proc. Camb. Phil. Soc. 66 365-370 (1969).
[2] Al. Salam, W. A . Some fractional q- integral and qderivatives. Proc. Edin. Math. Soc.17, 616-621 (1966).
[3] B.K. Dutta, L.K. Arora; On a Basic Analogue of Generalized H-function; International Journal of Mathematical Engineering and Science ISSN: 2277- 6982 Volume 1 Issue1(2010).
[4] Ernst, T. The history of q-calculus and new method (Licentiate Thesis), U.U.D.M. Report (2000).
[5] Gasper, G., Rahman, M.: Basic Hypergeometric Series, Cambridge University Press, Cambridge (1990).
[6] Jain D. K, R. Jain and Farooq Ahmad; Some Transformation Formula for Basic Analogue of Ifunction; Asian Journal of Mathematics and Statistics, 5(4), 158-162(2012)
[7] Kalla, S.L., Yadav, R.K., Purohit, S.D. On the Riemann-Liouville fractional q-integral operator involving a basic analogue of Fox H-function, Fract. Calc. Appl. Anal., 8(3), 313- 322 (2005).
[8] R.K. Yadav, S.D. Purohit, on fractions q-derivatives and transfunctions of the generalized basic hyper geometric functions, Indian Acad. Math. 28(1) 321-326.
[9] Saxena, R.K., Kumar, R. A Basic Analogue of the Generalized H-function, Le Matematiche, L, 263-271 (1995).
[10] Saxena, R.K., Modi, G.C. Kalla, S.L.: A basic analogue of Fox's H-function, Rev. Técn. Fac. Ingr. Univ. Zullia, 6, 139-143 (1983).
[11] Saxena, R.K. and Pogány, T.K. On fractional integration formulae for Aleph functions, Appl. Math. Comput.,218: 985-990(2011).
[12] Saxena, V.P.: The I-function, Anamaya Publishers, New Delhi (2008).
[13] Südland, N., Baumann, B., Nonnenmacher, T.F. Who knows about the Aleph ( H )- function?, Fract. Calc. Appl. Anal., 1(4), 401-402(1998).
[14] Südland, N., Baumann, B., Nonnenmacher, T.F: Fractional driftless 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, pp. 513-525 (2001).
[15] Yadav, R.K., Purohit, S.D.: On applications of Weyl fractional q-integral operator to generalized basic hypergeometric functions, Kyungpook Math.J. 46, 235- 245 (2006).
Naseer Ahmad Malik, "On a Basic Analogue of Generalized Hfunction with the help of fractional q-integral operator of Kober type," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 2, pp. 84-90, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P512