Sumudu transform

The Sumudu transform is an integral transform introduced in 1990 by G K Watagala. It is defined over the set of functions

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

where $p\le u\le q$, the Sumudu transform is defined as

$$S[f(t)]=\frac{1}{u}\underset{0}{\overset{\mathrm{\infty }}{\int }}f(t)\exp (-\frac{t}{u})dt.$$

Relationship with other transforms

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