The New Integral Transform: "NE Transform" and Its Applications

Abstract

This work introduces a new integral transform for functions of exponential order called “NE integral transform”. We prove some properties of NE -transform. Also, some applications of the NE- transform to find the solution to ordinary linear equation are given. The relationships of the new transform with well-known transforms are characterized by integral identities. We study the properties of this transform. Then we compare it with few exiting integral transforms in the Laplace family such as Laplace, Sumudu, Elzaki , Aboodh and etc. As well, the NE integral transform is applied and used to find the solution of linear ordinary differential equations.