On a new general integral transform: some properties and remarks

Abstract

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose in this paper we suggest a new kind of general integral transform and establish related main theorems.  The suggested transform which is called Ramadan Group (RG) transform and denoted by RGT is a hybrid of both Laplace and Sumudu transforms. The formula of the transform is defined and adopted as a standard general form.  A table of transformations to most popular functions is presented where we are in agreement with the case of Laplace and Sumudu transforms.