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Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
Some aspects of fractional diffusion equations of single and distributed order. (English)
[J] Appl. Math. Comput. 187, No. 1, 295-305 (2007). ISSN 0096-3003

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.
[K. C. Gupta (Jaipur)]

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
45K05 Integro-partial differential equations
60G18 Self-similar processes
60J60 Diffusion processes

Keywords: anomalous diffusion; fractional derivatives; integral transforms; Mellin-Barnes integrals; stochastic processes; asymptotic power laws

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