Geodesic
Some new generalized integral transformations and their application in differential equations theory
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 8-16

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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. 
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     title = {Some new generalized integral transformations and their application in differential equations theory},
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O. A. Repin; S. M. Zaikina. Some new generalized integral transformations and their application in differential equations theory. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 8-16. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a0/