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

$$A[f(t)]= \frac 1 u \int_0^\infty f(t) \exp\left(\frac1u\right) \, dt. $$

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