Abstract. In many papers, integral transforms have been introduced and found their application in solving certain boundary value problems. Indeed, as reference [1] shows, the natural transform is closely connected with Laplace and Sumudu transforms. In this paper we employ this transform to solving initial value problems of constant coefficients. Further, we discuss this transform on spaces of generalized functions. The distributional face of the natural transform is obtained as an analytic distribution. Whereas, the natural transform of a Boehmian is introduced by its limit in the distributional sense. More results are also established.

Received: February 8, 2013

AMS Subject Classification: 54C40, 14E20, 46E25, 20C20

Key Words and Phrases: natural transforms, differential equations, Sumudu transforms, Laplace transforms

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