DOI QR코드

DOI QR Code

GENERATING OPERATORS OF I-TRANSFORM OF THE MELLIN CONVOLUTION TYPE

  • Received : 2023.04.10
  • Accepted : 2023.08.08
  • Published : 2024.01.30

Abstract

In this paper, the I-transform of the Mellin convolution type is presented. Based on the Mellin transform theory, a general integral transform of the Mellin convolution type is introduced. The generating operators for I-transform together with the corresponding operational relations are also presented.

Keywords

Acknowledgement

Altaf A. Bhat and Faiza B. A. Suleiman extend their appreciation to the Dean and Head of research at University of Technology and Applied Sciences, Salalah, Oman for funding this work under internal Funded project. This work is supported by the Research project (JKST&IC/SRE/J/357-60) provided by JKST&IC, UT of J&K, India.

References

  1. Y. Luchko, Integral transforms of the Mellin convolution type and their generating operators, Int. Trans. Spec. Func. 19 (2008), 809-851. https://doi.org/10.1080/10652460802091617
  2. L. Debnath, D. Bhatta, Integral Transforms and Their Applications, CRC Press Taylor and Francis, Boca Raton, 2016.
  3. A.M. Mathai, H.J. Haubold, R.K. Saxena, The H-Function Theory and Applications, Springer, New York, London, 2010.
  4. H.M. Srivastava, R.G. Buschman, Mellin convolution and H-function transformations, Rock. Moun. J. Math. 6 (1976), 331-343.
  5. A. Kilicman, M.R.K. Ariffin, A note on the convolution in the Mellin sensewith generalized functions, Bull. Malay. Scie. Society 25 (2002), 93-100.
  6. M.A. Khan, Multiple Mellin convolution and I-function transform involving r variables, Int. J. Math. Research 1 (2012), 744-750.
  7. E.L. Koh, A.H. Zemanian, The complex Hankel and I-transform of generalized functions, SIAM J. Appl. Math. 6 (1968), 945-957. https://doi.org/10.1137/0116076
  8. N.X. Thao, T. Tuan, On the generalized convolution for I-transform, Acta Math. Vietnamica 28 (2003), 159-174.
  9. M. Garg, P. Manohar, S.L. Kalla, A Mittag-Leffler-type function of two variables, Int. Trans. Spec. Func. 24 (2013), 934-944. https://doi.org/10.1080/10652469.2013.789872
  10. T.K. Pogany, Some Mathieu-type series for the I-transform ocuring in the Fokker-Plank equation, Proy. J. Math. 30 (2011), 111-122.
  11. U.K. Saha, L.K. Arora, B.K. Dutta, Integrals involving I-function, Gen. Math. Notes 6 (2011), 1-14.
  12. V.P. Saxena, The I-Function, Anamaya Publishers, New Delhi, India, 2008.
  13. V.A. Kakichev, N.X. Thao, On the generalized convolution for H-transform, Izv. Vuzov. Math. 8 (1994), 21-28.
  14. A.P. Prudnikov, Y.A. Bruchkov, O.I. Marichev, Integral and Series. V.3, More Special Functions, Gordon and Breach Science Publishers, 1990.
  15. S.B. Yakubovich, N.T. Hai, Integral convolutions for H-transforms, Izv. Vuzov. Math. 8 (1991), 72-79.
  16. J. Pankaj, V.P. Saxena, Some new properties and inter-relation of Saxena's I-function, Doctoral Dissertations Jiwaji University Gwalior India, 2016.
  17. S.G. Samko, A.A. Kilbas, O.I. Marichev, Integral and Derivative of Fractional Order and Their Application, Gordon and Breach Science Publishers, 1993.
  18. I.N. Sneddon, Fourier Transform, Mc. Gray Hill, New York, 1951.
  19. S.B. Yakubovich, Y.F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer Science, Dordrecht, 1994.