The primary purpose of this research is to demonstrate an efficient replacement double transform called the Laplace–Sumudu (DLST) and prove some related theorems new transform. Also, we will discuss fundamental properties basic functions. Then, by utilizing those outcomes, apply it partial differential equations show its simplicity, efficiency, high accuracy.

In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition (SDM), then use to solve generalized Hirota-Satsuma Coupled kdv (H-SC kdv) systems also applied STM, find approximate solutions of system one. Then compare way exact solitary solutions. Clarifying best through tables d...

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

The main purpose of this work is to present a new double transform called the ARA-Sumudu (DARA-ST). application some basic functions and master properties are introduced. convolution existence theorems also presented proved. These results implemented obtain solution partial differential equations (PDEs), integral (IEs) functional equations. We formulas for solving families PDEs. latter ones use...