Geodesic
On Fractional Helmholtz Equations
Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 295-308

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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.
Keywords: Fractional Helmholtz Equation, Caputo Fractional Derivative, Weyl Fractional Derivative, Mittag-Leffler Function, Fox's H-function 
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     author = {Samuel, M. and Thomas, Anitha},
     title = {On {Fractional} {Helmholtz} {Equations}},
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Samuel, M.; Thomas, Anitha. On Fractional Helmholtz Equations. Fractional calculus and applied analysis, Tome 13 (2010) no. 3, pp. 295-308. http://geodesic.mathdoc.fr/item/FCAA_2010_13_3_a4/