Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 463579, 13 pages
doi:10.1155/2010/463579
Research Article

On a New Integral Transform and Differential Equations

A. Kiliçman1 and H. Eltayeb2

1Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
2Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 8 September 2009; Revised 5 April 2010; Accepted 6 May 2010

Academic Editor: Slimane Adjerid

Copyright © 2010 A. Kiliçman and H. Eltayeb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.