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Some aspects of fractional diffusion equations of single and distributed order. (English) Zbl 1122.26004
The paper deals with certain aspects of fractional diffusion equations of single and distributed order less than 1. The authors have stressed the importance of Fourier, Laplace and Mellin transforms and of functions of Mittag-Leffler and Wright in their study. First, they apply in either succession the Fourier transform in space and Laplace transform in time to the Cauchy problem. Next, they invert both the transforms by applying two strategies both leading to the same power series in the spatial variable with time-dependent coefficients. At the end, the authors provide an Appendix devoted to the notations used for two fractional derivatives used in the paper. This interesting paper also contains an extensive list of 40 references.

MSC:
26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
60G18 Self-similar stochastic processes
60J60 Diffusion processes
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