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

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.