# On the Relationship Between the Fractional Sumudu Transform and Fractional Fourier Transform

## Keywords:

Sumudu Transform, Fractional Sumudu transform, Fractional Laplace Transform, Fractional Mellin Transform, Fractional Fourier Transform## Abstract

In this paper we have discussed fractional Sumudu transforms and its relationship with fractional Fourier transform and obtained the mathematical expression of kernel of fractional Sumudu transform. Such findings will play a significant role for fractional Sumudu transform to recognize its importance in the fields of engineering and applied mathematics like other fractional transforms.

## References

. G. K. Watugala, “Sumudu transform: a new integral transform to solve differential equations and control engineering problems” Int. J. Math. Educ. Sci. Technol., Vol. 24, No. 1, 35-43 , 1993

. F.B.M Belgacem, A.A Karaballi “Sumudu transform fundamental properties investigations and applications. International Journal of Stochastic Analysis. Vol. 2006; 1-23, 2006.

. M. A. Asiru, “Further properties of the Sumudu transform and its applications,” International Journal of Mathematical Education in Science and Technology, vol. 33, no. 3, pp. 441–449, 2002.

. A. Kılıc¸man andH. Eltayeb, “A note on integral transforms and partial differential equations,” Applied Mathematical Sciences, vol. 4, no. 1–4, pp. 109–118, 2010.

. A. K,¸man, H. Eltayeb, and P. R. Agarwal, “On Sumudu transform and system of differential equations,” Abstract and Applied Analysis, vol. 2010, 2010.

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

. V. G. Gupta and B. Sharma, “Application of Sumudu transform in reaction-diffusion systems and nonlinear waves,” Applied Mathematical Sciences, vol. 4, no. 9–12, pp. 435–446, 2010.

. F. B. M. Belgacem, A. A. Karaballi, and S. L. Kalla, “Analytical investigations of the Sumudu transform and applications to integral production equations,” Mathematical Problems in Engineering, no. 3-4, pp. 103–118, 2003 .

. M. Baloch., S. Iqbal, The Relationship of Fractional Laplace Transform with Fractional Fourier, Mellin and Sumudu Transforms. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), 55(1), pp.11-16., 2019

. R. Silambarasan, K.S Nisar, et al “Discrete inverse Sumudu transform application to Whittaker and Zettl equations. AIP Conference Proceedings ,Vol. 2046, No. 1, p. 020091, 22018

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

. Gupta VG, Shrama B, Kiliçman A. A note on fractional Sumudu transform. Journal of Applied Mathematics, 2010

. K.K Sharma. Fractional Laplace transform, Springer-Verlag London, 377-379, 2010

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

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*American Scientific Research Journal for Engineering, Technology, and Sciences*,

*74*(1), 41–45. Retrieved from https://www.asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/6421

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