Sumudu transform explained

The Sumudu transform is an integral transform introduced in 1990 by G K Watagala.^{[1] [2] [3]} It is defined as the set as ^{[4] [5] [6]}

$$S\; =\; \backslash$$

where

and the Sumudu transform is defined as

$$A[f(t)]=\; \backslash frac\; 1\; u\; \backslash int\_0^\backslash infty\; f(t)\; \backslash exp\backslash left(\backslash frac1u\backslash right)\; \backslash ,\; dt.$$

Relationship with other transforms

And with u² Elzaki transform

Notes and 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 . 10.1080/0020739930240105 . 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 . en . 33 . 3 . 441–449 . 10.1080/002073902760047940 . 123671820 . 0020-739X.
3. Book: Zhang . Jun . Shen . Fangyang . Sumudu Transform for Automatic Mathematical Proof and Identity Generation . 2018 . Latifi . Shahram . Information Technology - New Generations . https://link.springer.com/chapter/10.1007/978-3-319-54978-1_85 . Advances in Intelligent Systems and Computing . 558 . en . Cham . Springer International Publishing . 677–683 . 10.1007/978-3-319-54978-1_85 . 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 . 10.1016/j.jfranklin.2010.03.008 . 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 . en . 24 . 1 . 35–43 . 10.1080/0020739930240105 . 0020-739X.
6. Kapoor . Mamta . June 15, 2023 . Sumudu Transform for Time Fractional Physical Models an Analytical Aspect . Journal of Applied Analysis & Computation . en . 13 . 3 . 1255–1273 . 10.11948/20220096 . 2156-907X. free .