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A perspective on fractional Laplace transforms and fractional generalized Hankel-Clifford transformation. (English) Zbl 1309.26009
Summary: In this study a relation between the Laplace transform and the generalized Hankel-Clifford transform is established. The relation between distributional generalized Hankel-Clifford transform 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 fractional Laplace and fractional generalized Hankel-Clifford transformation is proved in Zemanian space.
26A33 Fractional derivatives and integrals
44A10 Laplace transform
44A20 Integral transforms of special functions
46F12 Integral transforms in distribution spaces
Full Text: DOI
[1] [1] D. Rainville Earl, Special Functions, Chesla Publication Co. Bronx; (1960) NY.
[2] I.N. Sneddon, Use of Integral Transforms, T.M.H. Edition. (1979) · Zbl 0237.44001
[3] A.H. Zemanian, Generalized Integral Transformations, Interscience Publications, (1968) NY. · Zbl 0181.12701
[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.
[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.}
[6] B.R. Bhonsle, A relation between Laplace and Hankel transforms, journals.cambridge.org/article S2040618500034432.
[7] V. Namias, Fractionalisation of Hankel transform, J. Inst. Math. Appl., 26 (1980), 187{197.} · Zbl 0454.44001
[8] H. Bateman, Tables of integral transforms, Vol. II, McGraw-Hill book company Inc., New York (1954).
[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.}
[10] H. K. Fiona, A Fractional power theory for Hankel transforms, Int. J. of Mathematical Analysis and Application, 158 (1991), 114-123. · Zbl 0735.44002
[11] K.K. Sharma, Fractional Laplace transform, Journal of Signal, Image and Video Processing, Vol. 4 (2010), 377-379. · Zbl 1200.44002
[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. · Zbl 1192.46040
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