Schneider, W. R.; Wyss, W. Fractional diffusion and wave equations. (English) Zbl 0692.45004 J. Math. Phys. 30, No. 1, 134-144 (1989). Summary: Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with \(t^{\alpha -1}/\Gamma (\alpha)\), \(\alpha =1,2\), respectively. Fractional diffusion and wave equations are obtained by letting \(\alpha\) vary in (0,1) and (1,2), respectively. The corresponding Green’s functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown that the Green’s function of fractional diffusion is a probability density. Cited in 7 ReviewsCited in 422 Documents MSC: 45K05 Integro-partial differential equations 35K30 Initial value problems for higher-order parabolic equations Keywords:wave equations; convolution; Fractional diffusion; Green’s functions; Fox functions PDFBibTeX XMLCite \textit{W. R. Schneider} and \textit{W. Wyss}, J. Math. Phys. 30, No. 1, 134--144 (1989; Zbl 0692.45004) Full Text: DOI References: [1] DOI: 10.1063/1.527251 · Zbl 0632.35031 [2] Braaksma B. L. J., Compositio Math. 15 pp 239– (1964) [3] DOI: 10.1002/pssb.2221330150 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.