Sumudu transform

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]}

$${\displaystyle A=\{f(t):\ni M,p,q>0,|f(t)|=M\exp(1/u)\}}$$

where ${\displaystyle p\leq u\leq q}$, the Sumudu transform is defined as

$${\displaystyle S[f(t)]={\frac {1}{u}}\int _{0}^{\infty }f(t)\exp \left(-{\frac {t}{u}}\right)\,dt.}$$

Relationship with other transforms

Sumudu transform is 1/u Laplace transform ${\displaystyle S[f(t)](u)={\frac {1}{u}}L[f(t)]({\frac {1}{u}})}$ And with u² Elzaki transform ${\displaystyle S[f(t)](u)=u^{2}E[f(t)](u)}$

References

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.