Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 91083, 23 pages
doi:10.1155/JAMSA/2006/91083
Sumudu transform fundamental properties investigations and
applications
1Faculty of Information Technology, Arab Open University, P.O. Box 3322, Safat 13033, Kuwait
2Department of Mathematics
and Computer Science, Faculty of Science, Kuwait University, P.O.
Box 5969, Safat 13060, Kuwait
Received 3 May 2005; Revised 20 October 2005; Accepted 20 October 2005
Copyright © 2006 Fethi Bin Muhammed Belgacem and Ahmed Abdullatif Karaballi. 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
The Sumudu transform, whose fundamental properties are presented
in this paper, is still not widely known, nor used. Having scale
and unit-preserving properties, the Sumudu transform may be used
to solve problems without resorting to a new frequency domain. In
2003, Belgacem et al have shown it to be the theoretical dual to
the Laplace transform, and hence ought to rival it in problem
solving. Here, using the Laplace-Sumudu duality (LSD), we avail
the reader with a complex formulation for the inverse Sumudu
transform. Furthermore, we generalize all existing Sumudu
differentiation, integration, and convolution theorems in the
existing literature. We also generalize all existing Sumudu
shifting theorems, and introduce new results and recurrence
results, in this regard. Moreover, we use the Sumudu shift
theorems to introduce a paradigm shift into the thinking of
transform usage, with respect to solving differential equations,
that may be unique to this transform due to its unit-preserving
properties. Finally, we provide a large and more comprehensive
list of Sumudu transforms of functions than is available in the
literature.