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A general theorem for the generalized Weyl fractional integral operator involving the multivariable \(H\)-function. (English) Zbl 1065.26011

Summary: In this paper we establish a very general and useful theorem which interconnects the Laplace transform and the generalized Weyl fractional integral operator involving the multivariable \(H\)-function of related functions of several variables. Our main theorem involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values to these sequences, one can easily evaluate the generalized Weyl fractional integral operator of special functions of several variables. We have illustrated it for the Srivastava-Daoust multivariable hypergeometric function. On account of the general nature of this function a number of results involving special functions of one or more variables can be obtained merely by specializing the parameters.

MSC:

26A33 Fractional derivatives and integrals
33C65 Appell, Horn and Lauricella functions
44A10 Laplace transform
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