Sumudu transform

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

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

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 related to Laplace transform by the following relation: ${\displaystyle S[f(t)](u)={\frac {1}{u}}L[f(t)]({\frac {1}{u}})}$; and to Elzaki transform by the following relation: ${\displaystyle u^{2}S[f(t)](u)=E[f(t)](u)}$.

References