Natural Transform, Distribution theory, Convolution theorem
||The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications.
In this paper, we introduce the Natural transform in the generalized sense with the help of distribution theory. Inversion, Uniqueness theorems and some properties of generalized in¬tegral transform are proved.
Integral transform method has wide range of applications in the various fields of science and engineering. In most of the cases the physical phenomenon is converted into an ordinary differential equations and partial differential equations which can be solved by integral transform method. This is the basic thing by which the researchers are being motivated to define new integral transforms and used to solve many problems in the field of applied mathematics. Recently, the new integral transform Natural transform (N-transform) was introduced by (Khan and Khan, 2008) and studied its properties and some applications. Later on (Silambarasan et. al., 2011 and Belgacem et. al., 2012) defined the inverse Natural transform and studied some properties and applications of Natural transforms. The distribution theory provides powerful analytical technique to solve many problems that arises in the applied field. This gives rise to define the various integral transforms to the distribution space (Lookner, 2010, 2012 & 2013, Omari, 2014, Shah, 2015, Pathak, 1997, Schwartz, 1950, 51 and Zemanian, 1987).The aim of this paper is to extend the Natural transform in the distributional space of compact support and to investigate some properties and theorems of the generalized integral transform.
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In this paper we extended the Natural transform in the distributional space of compact support and so defined generalized Natural transform. The analyticity theorem and inversion theorem are proved. This paper might be a new window for the researcher to study of generalized integral transforms.
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