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Sub-diffusion equations of fractional order and their fundamental solutions. (English) Zbl 1135.35004

Taş, K. (ed.) et al., Mathematical methods in engineering. Selected papers of the international symposium, MME06, Ankara, Turkey, April 27–29, 2006. Dordrecht: Springer (ISBN 978-1-4020-5677-2/hbk; 978-1-4020-5678-9/e-book). 23-55 (2007).
In the present study the authors deal with some detail two cases of diffusion of distributed order: the double order and the uniformly distributed order discussing the differences between the Riemann-Liouville and Caputo approaches. For these cases the authors analyze in detail the behaviour of the fundamental solutions (numerically) and of the corresponding variance (analytically) through the exhibition of several plots. It is shown that, while for the Riemann-Liouville and for the Caputo cases the fundamental solutions seem not to differ too much for moderate times, the behaviour of the corresponding variance for small and large times differs in a remarkable way.
For the entire collection see [Zbl 1106.00005].

MSC:

35A08 Fundamental solutions to PDEs
26A33 Fractional derivatives and integrals
35C15 Integral representations of solutions to PDEs
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