an:05163934
Zbl 1122.26004
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf
Some aspects of fractional diffusion equations of single and distributed order
EN
Appl. Math. Comput. 187, No. 1, 295-305 (2007).
0096-3003
2007
j
26A33 45K05 60G18 60J60
anomalous diffusion; fractional derivatives; integral transforms; Mellin-Barnes integrals; stochastic processes; asymptotic power laws
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)