On a new integral transform and differential equations

International Journal of Analysis and Applications , 2019

In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed integral transform is successfully derived from the classical Fourier integral transform and is applied to both ordinary and partial differential equations to show its simplicity, efficiency, and the high accuracy.

2020

The primary purpose of this research is to demonstrate an efficient replacement double transform named the Laplace–Sumudu transform (DLST) to unravel integral differential equations. The theorems handling fashionable properties of the Laplace–Sumudu transform are proved; the convolution theorem with an evidence is mentioned; then, via the usage of these outcomes, the solution of integral differential equations is built.

2013

In this paper we have discussed Infinite Sumudu transform as well as Laplace transform was applied to solve linear ordinary differential equations with constant coefficients with convolution terms.

In the present paper authors introduce the L n-integral transform and the L −1 n inverse integral transform for n = 2 k , k ∈ N , as a generalization of the classical Laplace transform and the L −1 inverse Laplace transform, respectively. Applicability of this transforms in solving linear ordinary differential equations is analyzed. Some illustrative examples are also given.

2010

In this work a new integral transform, namely Sumudu transform was applied to solve linear ordinary differential equation with and without constant coefficients having convolution terms. In particular we apply Sumudu transform technique to solve Spring-Mass systems, Population Growth and financial problem.

Abstract and Applied Analysis, 2010

The regular system of differential equations with convolution terms solved by Sumudu transform.

2010

In this work we introduce some relationship between Sumudu and Laplace transforms, further; for the comparison purpose, we apply both transforms to solve differential equations to see the differences and similarities. Finally, we provide some examples regarding to second order differential equations with non constant coefficients as special case.

Sakarya University Journal of Science

One of the solution methods of ordinary and partial differential equations is integral transform. Newly introduced Sumudu transform provides an alternative integral transform which gives us an efficient tool to solve initial-boundary value problems. In this work, it is obtained solutions to some dynamic problems which arise in physics and engineering.

Global Journal of Pure and Applied Mathematics, 2012

In this paper we propose a novel computational algorithm for solving ordinary differential equations with non-constants coefficients by using the modified version of Laplace and Sumudu transforms which is called Elzaki transform. Elzaki transform can be easily applied to the initial value problems with less computational work. The several illustrative examples can not solve by Sumudu transform, this means that Elzaki transform is a powerful tool for solving some ordinary differential equations with variable coefficients.

IAETSD JOURNAL FOR ADVANCED RESEARCH IN APPLIED SCIENCES, 2018

Xiao-Jun Yang [1] proposes a new integral Transform called "Yang Transform" and applied to solve Steady Heat Transfer problem. In this paper researcher investigate the fundamental properties of Yang transform and used effectively to solve differential equations with constant coefficients. Also we define Laplace-Yang duality property.