Sumudu transform: a new integral transform to solve differential equations and control engineering problems

Abstract A new integral transform called the Sumudu transform is introduced. This transform possesses many interesting properties which make its visualization easier. Some of these properties are: (1) The differentiation and integration in the t‐domain is equivalent to division and multiplication of the transformed function F(u)by uin the u‐domain. (2) The unit‐step function in the t‐domain is transformed to unity in the u‐domain. (3) Scaling of the function f(t)in the t‐domain is equivalent to scaling of F(u) in the u‐domain by the same scale factor. (4) The limit of f(t) as ttends to zero is equal to the limit of F(u)as utends to zero. (5) For several cases, the limit of F(t)as ttends to infinity is the same as the limit of F(u)as u tends to infinity. (6) The slope of the function f(t) at t =0is the same as the slope of F(u) at u = 0. Hence uand F(u)are no longer dummies but can be treated as replicas of tand f(t).It is even possible to express uand F(u)using the units of tand f(t) respectively.