Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 591517, 13 pages
http://dx.doi.org/10.5402/2012/591517
Research Article

Some Remarks on the Sumudu and Laplace Transforms and Applications to Differential Equations

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

Received 10 October 2011; Accepted 20 November 2011

Academic Editor: K. Djidjeli

Copyright © 2012 Adem Kılıçman and Hassan 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

We study the relationship between Sumudu and Laplace transforms and further make some comparison on the solutions. We provide some counterexamples where if the solution of differential equations exists by Laplace transform, the solution does not necessarily exist by using the Sumudu transform; however, the examples indicate that if the solution of differential equation by Sumudu transform exists then the solution necessarily exists by Laplace transform.