MERICHEV-SAIGO-MAEDA FRACTIONAL INTEGRATION OPERATOR ASSOCIATED WITH SRIVASTAVA'S POLYNOMIAL AND GAUSS HYPERGEOMETRIC FUNCTIONS
Year 2017,
Volume: 5 Issue: 1, 145 - 160, 01.04.2017
D. L. Suthar
,
S. Agarwal
Abstract
The object of the present paper is to establish seven theorems for the Marichev-Saigo-Maeda operators of fractional integration of the product for the Srivastava polynomial with Gauss hypergeometric function. The theorems established in this paper are of general character and provide extension of the recently given by results Saxena, Ram and Suthar [11] and Singh and Singh [12]. Some interesting special cases of our main results are also considered.
References
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- [2] D. Kumar, P. Agarwal and S.D. Purohit, Generalized fractional integration of the H -function involving general class of polynomials, Walailak Journal of Science and Technology, 11(12) (2014), 1019-1030.
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- [6] J. Ram and Dinesh Kumar, Generalized fractional integration involving Appell Hypergeometric of the product of two H -functions, Vijanana Parishad Anusandhan Patrika, 54(2011), 33-43.
- [7] M. Saigo, A remark on integral operators involving the Guass hypergeometric function, Math. Rep. Kyushu Univ., 11(1977/78), no. 2, 135-143.
- [8] M. Saigo and N. Maeda, More generalization of fractional calculus, Transform methods & special functions, Varna '96, 386-400, Bulgarian Acad. Sci., Soa, (1998).
- [9] R.K. Saxena, On fractional integration operators, Math. Z., 96(1967), 289-291.
- [10] R.K. Saxena and M. Saigo, Generalized fractional calculus of the H-function associated with Appell function F3, J. Fract. Calc., 19(2001), 89-104.
- [11] R.K. Saxena, J. Ram and D.L. Suthar, Generalized fractional integration of the Gauss hypergeometric functions, Acta Cienc. Indica Math., 35(2009), no. 1, 281-292.
- [12] Lal Sahab Singh and Dharmendra Kumar Singh, Saigo operator of fractional integration involving the Gauss hypergeometric functions, Acta Cienc. Indica Math., 32(2006), no. 1, 427-434.
- [13] H.M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math., 14(1972), 1-6.
- [14] H.M. Srivastava and Per W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, (1985).
Year 2017,
Volume: 5 Issue: 1, 145 - 160, 01.04.2017
D. L. Suthar
,
S. Agarwal
References
- [1] D. Baleanu, D. Kumar and S.D. Purohit, Generalized fractional integrals of product of two H - functions and a general class of polynomials, International Journal of Computer Mathematics, 93, No. 8, (2016), 1320-1329.
- [2] D. Kumar, P. Agarwal and S.D. Purohit, Generalized fractional integration of the H -function involving general class of polynomials, Walailak Journal of Science and Technology, 11(12) (2014), 1019-1030.
- [3] D. Earl Rainville, Special Function, The Macmillan, New York, (1960).
- [4] E. George, C. Andrews Larry, Special function for Engineering and Applied Mathematics, Macmillan, New York, (1985).
- [5] S.L. Kalla and R.K. Saxena, Integral operators involving hypergeometric functions, Math. Z. 108(1969), 231-234.
- [6] J. Ram and Dinesh Kumar, Generalized fractional integration involving Appell Hypergeometric of the product of two H -functions, Vijanana Parishad Anusandhan Patrika, 54(2011), 33-43.
- [7] M. Saigo, A remark on integral operators involving the Guass hypergeometric function, Math. Rep. Kyushu Univ., 11(1977/78), no. 2, 135-143.
- [8] M. Saigo and N. Maeda, More generalization of fractional calculus, Transform methods & special functions, Varna '96, 386-400, Bulgarian Acad. Sci., Soa, (1998).
- [9] R.K. Saxena, On fractional integration operators, Math. Z., 96(1967), 289-291.
- [10] R.K. Saxena and M. Saigo, Generalized fractional calculus of the H-function associated with Appell function F3, J. Fract. Calc., 19(2001), 89-104.
- [11] R.K. Saxena, J. Ram and D.L. Suthar, Generalized fractional integration of the Gauss hypergeometric functions, Acta Cienc. Indica Math., 35(2009), no. 1, 281-292.
- [12] Lal Sahab Singh and Dharmendra Kumar Singh, Saigo operator of fractional integration involving the Gauss hypergeometric functions, Acta Cienc. Indica Math., 32(2006), no. 1, 427-434.
- [13] H.M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math., 14(1972), 1-6.
- [14] H.M. Srivastava and Per W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, (1985).