On a New Integral Transform and Differential Equations

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, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, it was proved that Sumudu transform has very special and useful properties. In this paper we study this interesting integral transform and its efficiency in solving the linear ordinary differential equations with constant and nonconstant coefficients as well as system of differential equations.

A new integral transform on time scales and its applications

“…The results in this article not only can be applied to ordinary differential equations when T = R, difference equations when T = N 0 , but also, can be applied for q-difference equations when T = q N 0 , where q N 0 := {q t : t ∈ N 0 for q > 1} or T = q Z := q Z ∪ {0} for q>1 which has several important applications in quantum theory and on different types of time scales like T = hN 0 , T = N 2 0 , and T = T n the space of the harmonic numbers. Regarding the comparison between Sumudu and Laplace transform, see for example, [4][5][6][7]16]. For example when T = R, Maxwell's equations were solved for transient electromagnetic waves propagating in lossy conducting media, see [16] where the Sumudu transform of Maxwell's differential equations yields a solution directly in the time domain, which neutralizes the need to perform the inverse Sumudu transform.…”

“…Watugala [1,2] introduced a new integral transform and named it the Sumudu transform that is defined by the formula However in [3,4], some fundamental properties of the Sumudu transform were established. By looking at the properties of this transform one can notice that the Sumudu transform has very special and useful properties and it can help with intricate applications in the sciences and engineering.…”

Exact solutions for linear systems of local fractional partial differential equations

“…These systems were formally derived to describe wave propagation, to control the shallow water waves, and to examine the chemical reaction-diffusion model of Brusselator [1]. To solve these equations or systems, researchers use many methods, among them, we find an Adomian decomposition method (ADM) [2], homotopy perturbation method (HPM) [3], variational iteration method (VIM) [4], Fourier transform method [5], Fourier series method [6], Laplace transform method [7], and Sumudu transform method [8], and then extended it to solve differential equations of fractional orders. Recently, there appeared a large part of scientific research concerning local fractional differential equations or local fractional partial differential, adopted in its entirety on the above mentioned methods to solve this new types of equations.…”

On double Natural transform and its applications

“…Sumudu transform was first introduced by [30] and some of its applications were given by [2,14,20,22]. For more information and features regarding Sumudu transform we refer to [3][4][5][6].…”