Sumudu transform

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

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

where $p\leq u\leq q$

and the Sumudu transform is defined as

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

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 $S[f(t)](u)=u^{2}E[f(t)](u)$