International Journal of Mathematics Trends and Technology
Volume 61 | Number 2 | Year 2018 | Article Id. IJMTT-V61P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P511
In the present paper, we derive two theorem involving fractional q-integral operators of Erdélyi-Kober type and a basic of Aleph-function of two variables. Corresponding assertions for the Riemann-Liouville and Weyl fractional q-integral transforms are also presented. Several special cases of the main results have been illustrated in the concluding section.
[1] M.H. Abu-Risha, M.H. Annaby, M.E.H. Ismail and Z.S. Mansour, Linear q-difference equations, Z. Anal. Anwend. 26 (2007), 481-494.
[2] R.P. Agarwal, Certain fractional q-integrals and q-derivatives, Proc. Camb. Phil. Soc., 66(1969), 365-370.
[3] W.A. Al-Salam, Some fractional q-integrals and q-derivatives, Proc. Edin. Math. Soc., 15(1966), 135-140.[4] G.
[4] D.K. Choudary, Generalized fractional differintegral operators of the Aleph-function of two variables, Journal of Chemical, Biological and Physical Sciences, Section C, 6(3) (2016), 1116-1131.
[5] Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cam-bridge, 1990.
[6] L. Galue, Generalized Weyl fractional q-integral operator, Algebras, Groups Geom., 26 (2009), 163-178.
[7] L. Galue, Generalized Erdelyi-Kober fractional q-integral operator, Kuwait J. Sci. Eng., 36 (2A) (2009), 21-34.
[8] S.L. Kalla, R.K. Yadav and S.D. Purohit, On the Riemann-Liouville fractional q-integral operator involving a basic analogue of Fox H-function, Fract. Calc. Appl. Anal., 8(3) (2005), 313-322.
[9] K.C. Gupta, and P.K. Mittal, Integrals involving a generalized function of two variables, (1972), 430-437.
[10] Z.S.I. Mansour, Linear sequential q-difference equations of fractional order, Fract. Calc. Appl. Anal., 12(2) (2009), 159-178.
[11] P.K. Mittal and K.C. Gupta, On a integral involving a generalized function of two variables, Proc. Indian Acad. Sci. 75A (1971), 117-123
[12] R.K. Saxena, G.C. Modi and S.L. Kalla, A basic analogue of H-function of two variable, Rev. Tec. Ing. Univ. Zulia, 10(2) (1987), 35-38.
[13] R.K. Saxena, R.K. Yadav, S.L. Kalla and S.D. Purohit, Kober fractional q-integral operator of the basic analogue of the H-function, Rev. Tec. Ing. Univ. Zulia, 28(2) (2005), 154-158.
[14] C.K. Sharma and P.L. Mishra, On the I-function of two variables and its Certain properties, Acta Ciencia Indica, 17 (1991), 1-4.
[15] K. Sharma, On the Integral Representation and Applications of the Generalized Function of Two Variables, International Journal of Mathematical Engineering and Science, 3(1) (2014), 1-13.
[16] R.K. Yadav and S.D. Purohit, On application of Kober fractional q-integral operator to certain basic hypergeometric function, J. Rajasthan Acad. Phy. Sci., 5(4) (2006), 437-448.
[17] R.K. Yadav and S.D. Purohit, On applications of Weyl fractional q-integral operator to generalized basic hypergeometric functions, Kyungpook Math. J., 46 (2006), 235-245.
[18] R.K. Yadav, S.D. Purohit and S.L. Kalla, On generalized Weyl fractional q-integral operator involving generalized basic hypergeometric function, Fract. Calc. Appl. Anal., 11(2) (2008),129-142.
[19] R.K. Yadav, S.D. Purohit, S.L. Kalla and V.K. Vyas, Certain fractional q-integral formulae for the generalized basic hypergeometric functions of two variables, Jourla of Inequalities and Special functions, 1(1) (2010), 30-38.
F.Y.Ayant, "Certain Fractional Q-Derivative Integral Formulae for the Basic Aleph-Function of Two Variables," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 2, pp. 78-84, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P511
PDF 
Abstract 
Keywords 
References 
Citation