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Sumudu transform: A new integral transform to solve differential equations and control engineering problems. (English) Zbl 0768.44003
The author modifies the Laplace transform in the following form $F\left(u\right)=\left(1/u\right){\int }_{0}^{\infty }{e}^{-t/u}f\left(t\right)dt$, so that $u$ and $F\left(u\right)$ are no longer dummies but can be treated as replicas of $t$ and $f\left(t\right)$. It is even possible to express them in the same units as $t$ and $f\left(t\right)$ so that the consistency of units in a differential equation describing a physical process can be maintained even after transformation. A few properties of the modified transform are given and two applications are included as examples.

##### MSC:
 44A15 Special transforms (Legendre, Hilbert, etc.) 34A25 Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.) 44A10 Laplace transform