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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

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Mathematical Citation Quotient (MCQ) 2016: 0.14

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1512-0139
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A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation

V. R. Lakshmi Gorty
  • Corresponding author
  • SVKM's NMIMS University, MPSTME, Vile Parle (W), Mumbai, Maharashtra 400056, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-02-23 | DOI: https://doi.org/10.1515/tmj-2015-0004

Abstract

In this study a relation between the Laplace transform and the generalized Hankel-Clifford transform is established. The relation between distributional generalized Hankel-Clifford trans- form and distributional one sided Laplace transform is developed. The results are verified by giving illustrations. The relation between fractional Laplace and fractional generalized Hankel-Clifford transformation is also established. Further inversion theorem considering frac- tional Laplace and fractional generalized Hankel-Clifford transformation is proved in Zemanian space.

Keywords: Generalized Hankel-Clifford transforms; Laplace Transforms; generalized Hankel-Clifford inversion theorem; test- ing function space for generalized Hankel-Clifford transform and Laplace transforms; fractional Laplace transforms and fractional generalized Hankel-Clifford transformation.

References

  • [1] D. Rainville Earl, Special Functions, Chesla Publication Co. Bronx; (1960) NY. Google Scholar

  • [2] I.N. Sneddon, Use of Integral Transforms, T.M.H. Edition. (1979) Google Scholar

  • [3] A.H. Zemanian, Generalized Integral Transformations, Interscience Publications, (1968) NY. Google Scholar

  • [4] S. P. Malgond, and V. R. Lakshmi Gorty, The generalized Hankel-Clifford transformation on M′α and its representation, IEEE Xplore Digital Library (2013), http://ieeexplore.ieee.org , page(s): 1-9. Google Scholar

  • [5] S .K. Panchal, Relation between Hankel and Laplace transforms of distributions, Bulletin of the Marathwada Mathematical Society, Vol. 13, No. 1 (2012), 30{32. Google Scholar

  • [6] B.R. Bhonsle, A relation between Laplace and Hankel transforms, journals.cambridge.org/article S2040618500034432. Google Scholar

  • [7] V. Namias, Fractionalisation of Hankel transform, J. Inst. Math. Appl., 26 (1980), 187{197. Google Scholar

  • [8] H. Bateman, Tables of integral transforms, Vol. II, McGraw-Hill book company Inc., New York (1954). Google Scholar

  • [9] D. Z. Fange and W. Shaomi, Fractional Hankel transform and the diffraction of misaligned optical systems, J. of Modern optics, Vol. 52, No.1 (2005), 61{71. Google Scholar

  • [10] H. K. Fiona, A Fractional power theory for Hankel transforms, Int. J. of Mathematical Analysis and Application, 158 (1991), 114-123. Google Scholar

  • [11] K.K. Sharma, Fractional Laplace transform, Journal of Signal, Image and Video Processing, Vol. 4 (2010), 377-379. Google Scholar

  • [12] R.D. Taywade, A.S. Gudadhe and V.N. Mahalle, Inversion of Fractional Hankel Transform in the Zemanian Space, International Conference on Benchmarks in Engineering Science and Technology ICBEST (1991); page 31-34. Google Scholar

About the article

Published Online: 2015-02-23


Citation Information: Tbilisi Mathematical Journal, Volume 8, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2015-0004.

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© 2015 V. R. Lakshmi Gorty. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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