Modified Sumudu Transform and Its Properties

Year 2021, , 389 - 396, 15.04.2021

Uğur Duran

https://doi.org/10.16984/saufenbilder.825180

Cited By: 4

Abstract

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

Keywords

gamma function, laplace transform, sumudu transform, convolution

References

• [1] M. U. 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.
• [2] 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, vol. 2003, no.3, pp. 103-118, 2003.
• [3] F. B. M. Belgacem, "Introducing and analysing deeper Sumudu properties," Nonlinear Studies, vol. 13, no.1, pp. 23-41, 2006.
• [4] F. B. M. Belgacem, Karaballi, A. A. "Sumudu transform fundamental properties investigations and applications," International Journal of Stochastic Analysis, article id 91083, pp. 1-23, 2016.
• [5] L. Debnath, "Integral Transforms and Their Applications," CRC Press, Florida, 1995.
• [6] A. Kilicman, H. E. Gadian, "On the application of Laplace and Sumudu transforms," Journal of The Franklin Institute, vol. 347, pp. 848-862, 2010.
• [7] A. D. Poularikas, "The Transforms and Applications Handbook, The Electrical Engineering Handbook Series" CRC Press, Florida, 1996.
• [8] R. Saadeh, A. Qazza, A. Burqan, "A New Integral Transform: ARA Transform and Its Properties and Applications," Symmetry, vol. 12, article no.925, 2020.
• [9] M. Saif, F. Khan, K. S. Nisar, S. Araci, "Modified Laplace transform and its properties," Journal of Mathematics and Computer Science, vol. 21, no.2, pp. 127-135, 2020.
• [10] G. K. Watugula, "Sumudu transform: A new integral transform to solve differential equations and control engineering problems," International Journal of Mathematical Education in Science and Technology, vol. 24, pp. 35-43, 1993.
• [11] G. K. Watagula, "The Sumudu transform for functions of two variables," Mathematical Engineering in Industry, vol. 8, no.4, pp. 293-302, 2002.
• [12] S. Weerakoon, "Application of Sumudu transform to partial differential equations," International Journal of Mathematical Education in Science and Technology, vol. 25, no.2, pp. 277-283, 1994.