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On fractional Helmholtz equations. (English) Zbl 1223.26013

Summary: In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox’s \(H\)-function.

MSC:

26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
35R11 Fractional partial differential equations
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