Some aspects of fractional diffusion equations of single and distributed order

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dc.creatorMainardi, Francesco
dc.creatorPagnini, Gianni
dc.creatorGorenflo, Rudolf
dc.date2007-11-27
dc.date.accessioned2026-07-07T09:40:45Z
dc.date.available2026-07-07T09:40:45Z
dc.descriptionThe time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $β\in (0,1)$. The fundamental solution for the Cauchy problem is interpreted as a probability density of a self-similar non-Markovian stochastic process related to a phenomenon of sub-diffusion (the variance grows in time sub-linearly). A further generalization is obtained by considering a continuous or discrete distribution of fractional time derivatives of order less than one. Then the fundamental solution is still a probability density of a non-Markovian process that, however, is no longer self-similar but exhibits a corresponding distribution of time-scales.
dc.description14 pages. International Symposium on "Analytic Function Theory, Fractional Calculus and Their Applications", University of Victoria (British Columbia, Canada), 22-27 August 2005
dc.identifierhttps://arxiv.org/abs/0711.4261
dc.identifierhttp://arxiv.org/abs/0711.4261
dc.identifierApplied Mathematics and Computation, Vol. 187, No 1, pp. 295-305 (2007)
dc.identifierdoi:10.1016/j.amc.2006.08.126
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161584
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subject26A33, 44A10, 45K05, 60G18, 60J60
dc.titleSome aspects of fractional diffusion equations of single and distributed order
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