The Relationship of Fractional Laplace Transform with Fractional Fourier, Mellin and Sumudu Transforms

  • Maria Baloch Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Saleem Iqbal Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
  • Farhana Sarwar Department of Mathematics F.G.Girls Degree College, Madrissa Road , Quetta, Cantt, 87300, Pakistan
  • Abdul Rehman Abdul Rehman Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan
Keywords: Fractional Laplace Transform, Fractional Mellin Transform, Fractional Fourier Transform, Fractional Sumudu transform.

Abstract

We have developed in this research paper, some of the fundamental relationship of fractional Laplace transform with fractional Fourier, fractional Mellin and fractional Sumudu transforms. These results are expressed mathematically, and such relationships should be very useful in applications to signal processing and optics.

References

V. Namias, “The fractional order Fourier transform and its application to quantum mechanics”, IMA Journal of Applied Mathematics, 25(3) (1980) 241-265

A. Torre. (2003). Linear and Radial Canonical Transforms of Fractional Order. Computational and Applied Mathematics, 477-486.

P. R.Gudadhe, Analytical study of a special case of complex canonical transform. Global Journal of Mathematical Sciences, (2010) 293-302

G.Jumarie, Fractional Laplace transform with Mittage Leffler function. Applied Mathematics, (2009).

K.K Sharma. Fractional Laplace transform, Springer-Verlag London Limited, 4, (2010) 377-379

R.Prabhakar, Deshmukhi, S.D. Alka, Convolution structure for two version of fractional Laplace Transform, Journal of Science and Arts, 2(15),(2011) 143-150.

R. A. Treumann, W. Baumjohann, Fractional Laplace transform-A Perspective, Frontier Physics, 2,(2014). 1-4. Institute for Nonlinear Science. Springer, New York, NY (2003)

L.B. Almeida, “The fractional Fourier transform and time-frequency representations”, IEEE Transactions on Signal Processing, 42(11) (1994) 3084–3091

A. Peng, Y. Wang, X. Zuo, L. Gong, Properties of fractional Mellin transform, Advances in Information Sciences and Services Sciences 5(11) (2013) 90-96.

Keji Li, Y. X. (2011). A brief introduction of Sumudu transform and comparison with other integral transforms. IEEE, 285-287.

Gupta, V.J et el. (2010). A note of fractional Sumudu Transform, journal of Applied Mathematics Research Article (9 pages), Article ID 154189, Volume 2010.

Published
2019-04-25
Section
Articles