Geodesic
Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative
Fractional calculus and applied analysis, Tome 8 (2005) no. 4, pp. 403-430.

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The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
Keywords: Diffusion-Wave Equation of Fractional Order, Riemann-Liouville Partial Fractional Derivative, Cauchy-Type Problem, H-Function, Mittag-Leffler and Wright Functions, Fourier and Laplace Transforms, 35A15, 44A15, 26A33 
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     title = {Cauchy-Type {Problem} for {Diffusion-Wave} {Equation} with the {Riemann-Liouville} {Partial} {Derivative}},
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Kilbas, Anatoly; Trujillo, Juan; Voroshilov, Aleksandr. Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative. Fractional calculus and applied analysis, Tome 8 (2005) no. 4, pp. 403-430. http://geodesic.mathdoc.fr/item/FCAA_2005_8_4_a4/