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Sumudu transform
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The Sumudu transform is an integral transform introduced in 1990 by G K Watagala.[1][2][3] It is defined over the set of functions [4][5][6]
where , the Sumudu transform is defined as
![{\displaystyle S[f(t)]={\frac {1}{u}}\int _{0}^{\infty }f(t)\exp \left(-{\frac {t}{u}}\right)\,dt.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37bc2fa3194110842d04e38b797305d1a5874ad1)
Relationship with other transforms
[edit]Sumudu transform is 1/u Laplace transform And with u2 Elzaki transform
={\frac {1}{u}}L[f(t)]({\frac {1}{u}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e5d7fb53a3c3da35d1fc63d8236df53ef50d41e)
=u^{2}E[f(t)](u)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1224e9b7dcbb974ceb0acb38a4d1b4f5ee71c3ce)
References
[edit]- ^ Watugala, G. K. (January 1993). "Sumudu transform: a new integral transform to solve differential equations and control engineering problems". International Journal of Mathematical Education in Science and Technology. 24 (1): 35–43. doi:10.1080/0020739930240105. ISSN 0020-739X.
- ^ Asiru, Muniru Aderemi (May 2002). "Further properties of the Sumudu transform and its applications". International Journal of Mathematical Education in Science and Technology. 33 (3): 441–449. doi:10.1080/002073902760047940. ISSN 0020-739X. S2CID 123671820.
- ^ Zhang, Jun; Shen, Fangyang (2018). "Sumudu Transform for Automatic Mathematical Proof and Identity Generation". In Latifi, Shahram (ed.). Information Technology - New Generations. Advances in Intelligent Systems and Computing. Vol. 558. Cham: Springer International Publishing. pp. 677–683. doi:10.1007/978-3-319-54978-1_85. ISBN 978-3-319-54978-1.
- ^ Kılıcman, A.; Gadain, H. E. (2010-06-01). "On the applications of Laplace and Sumudu transforms". Journal of the Franklin Institute. 347 (5): 848–862. doi:10.1016/j.jfranklin.2010.03.008. ISSN 0016-0032.
- ^ Watugala, G. K. (January 1993). "Sumudu transform: a new integral transform to solve differential equations and control engineering problems". International Journal of Mathematical Education in Science and Technology. 24 (1): 35–43. doi:10.1080/0020739930240105. ISSN 0020-739X.
- ^ Kapoor, Mamta (June 15, 2023). "Sumudu Transform for Time Fractional Physical Models an Analytical Aspect". Journal of Applied Analysis & Computation. 13 (3): 1255–1273. doi:10.11948/20220096. ISSN 2156-907X.