A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

doi:10.1016/S0252-9602(15)30061-8

Abstract

Abstract:

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, include (for example) existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

Key words: Laplace transform, Sumudu transform, natural transform, H-function, H-transform, inversion formula, Parseval-type relationship, existence theorem, Borel-D?, rbashjan transform, Fubini's theorem, Weierstrass's test, Heaviside generalized function

CLC Number:

33C60

H. M. SRIVASTAVA, Minjie LUO, R. K. RAINA. A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS[J].Acta mathematica scientia,Series B, 2015, 35(6): 1386-1400.

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