Applications of sumudu transformation to some partial differential equations

In this study, the properties of Sumudu transform and its applications are explained. In addition, the Laplace transform and its properties are considered; The relationship between Sumudu and Laplace transformations is examined and the theorem which shows this relation is given. Sumudu transform with the article [5], it is a transformation presented by Watugala in 1993 and has an important role in solving some ordinary differential equations in control engineering. In this study, Sumudu transformation is applied to ordinary differential equations and partial differential equations and equations systems are solved in a simpler way. In the first parts of the study, the basic information for the integral transformations, the basic properties of the Laplace and Sumudu transformations are given Derivatives and integrals of Sumudu transformation were taken. In the following chapters, the solution of equation systems was obtained by applying the Sumudu transform to appropriate ordinary differential equations and partial differential equations. Particularly the first and second order partial differential equations were applied to Sumudu transformations and they were carried out for the purpose of the study. Keywords: Laplace transform, Sumudu transform, derivative of Sumudu transform, integral of Sumudu transform, integral transforms, differential equation, partial differential equation, convolution.