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Year 2019, Volume 9, Issue 4, 822 - 829, 01.12.2019

Abstract

References

  • Chaudhry, M. A., Qadir, A., Rafique, M. and Zubair, S. M., (1997), Extension of Euler’s Beta function, J. Comput. Appl. Math., 78, pp. 19-32.
  • Chaudhry, M. A., Qadir, A., Srivastava, H. M. and Paris, R. B., (2004), Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159, pp. 589-602.
  • Choi, J., Rathie, A. K. and Parmar, R. K., (2014), Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Math. J., 36(2), pp. 339-367.
  • Erd´elyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., (1953), Higher Transcendental Func- tions, Vol.1, McGraw-Hill, New York.
  • Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., (2006), Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York.
  • Lee, D. M., Rathie, A. K., Parmar, R. K. and Kim, Y. S., (2011), Generalization of extended Beta function, hypergeometric and confluent hypergeometric functions, Honam Math. J., 33, pp. 187-206.
  • Mathai, A. M. and Saxena, R. K., (1973), Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes Series No. 348, Springer-Verlag, Berlin, New York. Heidelberg, Germany.
  • Mathai, A. M., Saxena, R. K. and Haubold, H. J., (2010), The H-Functions: Theory and Applications, Springer, New York.
  • Parmar, R. K., (2013), A new generalization of Gamma, Beta, hypergeometric and confluent hyper- geometric functions, Matematiche (Catania), 69, pp. 33-52.
  • Parmar, R. K., (2014), Some generating relations for generalized extended hypergeometric functions involving generalized fractional derivative operator, J. Concr. Appl. Math., 12, pp. 217-228.
  • Parmar, R. K. and Purohit, S. D., (2017), Certain integral transforms and fractional integral formulas for the extended hupergeometric functions, TWMS J. Appl. Engg. Math., 7(1), In press.
  • Pohlen, T., (2009), The Hadamard Product and Universal Power Series, Dissertation, Universit¨at Trier.
  • Prudnikov, A. P., Brychkov, Yu. A. and Marichev, O.I., (1992), Integrals and Series. Special Functions, Vol. 1-5, Gordon and Breach., New York.
  • Saigo, M., (1978), A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11, pp. 135-143.
  • Saigo, M. and Maeda, N., (1996), More generalization of fractional calculus, Transform Methods and Special Function, Verna Bulgaria, pp. 386-400.
  • Srivastava, H.M., (1972), A contour integral involving Fox’s H-function, Indian J. Math., 14, pp. 1-6.
  • Srivastava, H. M. and Karlsson, P. W., (1985), Multiple Gaussian Hypergeometric Series, Halsted Press, (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto.
  • Srivastava, H. M., Parmar, R. K. and Chopra, P., (2012), A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions, Axioms, 1, pp. 238- 258.
  • Srivastava, H. M. and Saxena, R. K., (2001), Operators of fractional integration and their applications, Appl. Math. Comput., 118, pp. 1-52.

FRACTIONAL INTEGRALS FOR THE PRODUCT OF SRIVASTAVA'S POLYNOMIAL AND p, q -EXTENDED HYPERGEOMETRIC FUNCTION

Year 2019, Volume 9, Issue 4, 822 - 829, 01.12.2019

Abstract

The main object of this paper is to present certain new image formulas for the product of general class of polynomial and p; q {extended Gauss's hypergeometric function by applying the Saigo-Maeda fractional integral operators involving Appell's function F3. Certain interesting special cases of our main results are also considered.

References

  • Chaudhry, M. A., Qadir, A., Rafique, M. and Zubair, S. M., (1997), Extension of Euler’s Beta function, J. Comput. Appl. Math., 78, pp. 19-32.
  • Chaudhry, M. A., Qadir, A., Srivastava, H. M. and Paris, R. B., (2004), Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159, pp. 589-602.
  • Choi, J., Rathie, A. K. and Parmar, R. K., (2014), Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Math. J., 36(2), pp. 339-367.
  • Erd´elyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., (1953), Higher Transcendental Func- tions, Vol.1, McGraw-Hill, New York.
  • Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., (2006), Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York.
  • Lee, D. M., Rathie, A. K., Parmar, R. K. and Kim, Y. S., (2011), Generalization of extended Beta function, hypergeometric and confluent hypergeometric functions, Honam Math. J., 33, pp. 187-206.
  • Mathai, A. M. and Saxena, R. K., (1973), Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes Series No. 348, Springer-Verlag, Berlin, New York. Heidelberg, Germany.
  • Mathai, A. M., Saxena, R. K. and Haubold, H. J., (2010), The H-Functions: Theory and Applications, Springer, New York.
  • Parmar, R. K., (2013), A new generalization of Gamma, Beta, hypergeometric and confluent hyper- geometric functions, Matematiche (Catania), 69, pp. 33-52.
  • Parmar, R. K., (2014), Some generating relations for generalized extended hypergeometric functions involving generalized fractional derivative operator, J. Concr. Appl. Math., 12, pp. 217-228.
  • Parmar, R. K. and Purohit, S. D., (2017), Certain integral transforms and fractional integral formulas for the extended hupergeometric functions, TWMS J. Appl. Engg. Math., 7(1), In press.
  • Pohlen, T., (2009), The Hadamard Product and Universal Power Series, Dissertation, Universit¨at Trier.
  • Prudnikov, A. P., Brychkov, Yu. A. and Marichev, O.I., (1992), Integrals and Series. Special Functions, Vol. 1-5, Gordon and Breach., New York.
  • Saigo, M., (1978), A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11, pp. 135-143.
  • Saigo, M. and Maeda, N., (1996), More generalization of fractional calculus, Transform Methods and Special Function, Verna Bulgaria, pp. 386-400.
  • Srivastava, H.M., (1972), A contour integral involving Fox’s H-function, Indian J. Math., 14, pp. 1-6.
  • Srivastava, H. M. and Karlsson, P. W., (1985), Multiple Gaussian Hypergeometric Series, Halsted Press, (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto.
  • Srivastava, H. M., Parmar, R. K. and Chopra, P., (2012), A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions, Axioms, 1, pp. 238- 258.
  • Srivastava, H. M. and Saxena, R. K., (2001), Operators of fractional integration and their applications, Appl. Math. Comput., 118, pp. 1-52.

Details

Primary Language English
Journal Section Research Article
Authors

D. L. SUTHAR This is me
Department of Mathematics, Wollo University, Dessie, P.O. Box: 1145, Amhara Region, Ethiopia.


L. N. MİSHRA This is me
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT). University, Vellore 632 014, Tamil Nadu, India.


A. M. KHAN This is me
Department of Mathematics, JIET Group of Institutions, Jodhpur, Rajasthan, India.


A. ALARİ This is me
Department of Mathematics, Poornima University, Jaipur, Rajasthan, India.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760954, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {822 - 829}, title = {FRACTIONAL INTEGRALS FOR THE PRODUCT OF SRIVASTAVA'S POLYNOMIAL AND p, q -EXTENDED HYPERGEOMETRIC FUNCTION}, key = {cite}, author = {Suthar, D. L. and Mishra, L. N. and Khan, A. M. and Alari, A.} }