This article is cited in 2 papers

Differential Equations

Some new generalized integral transformations and their application in differential equations theory

O. A. Repin^ab, S. M. Zaikina<sup>ca

a</sup> Dept. of Applied Mathematics and Computer Science, Samara State Technical University, Samara
^b Dept. of Mathematical Statistics and Econometrics, Samara State Economic University, Samara
^c Dept. of Computer Science and Experimental Mathematics, Volgograd State University, Volgograd

Abstract: We present new integral transforms, generalized the classical Laplace, Stieltjes and Widder integral transforms in the potential theory. The $(\tau,\beta)$-generalized confluent hypergeometric functions are the kernels of these integral transforms. Inverse formulas for new integral transforms are proved. Relations of the Parseval–Goldstein type are established. Some examples of applications of the new integral transforms are given.

Keywords: integral transforms, Parseval–Goldstein type identity, inversion theorems.

UDC: 517.581

MSC: Primary 33C15; Secondary 44A15

Original article submitted 29/XII/2010
revision submitted – 20/IV/2011

DOI: 10.14498/vsgtu913

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