Time-fractional diffusion of distributed order

Details Time-fractional diffusion of distributed order Time-fractional diffusion of distributed order

2007-01-07

arxiv.org/abs/cond-mat/0701132v2

Physics

Condensed Matter

Statistical Mechanics

30 pages, 4 figures. International Workshop on Fractional Differentiation and its Applications (FDA06), 19-21 July 2006, Porto

Scientific paper

The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of time orders we provide the fundamental solution, that is still a probability density, in terms of an integral of Laplace type. The kernel depends on the type of the assumed fractional derivative except for the single order case where the two approaches turn to be equivalent. We consider with some detail two cases of order distribution: the double-order and the uniformly distributed order. For these cases we exhibit plots of the corresponding fundamental solutions and their variance, pointing out the remarkable difference between the two approaches for small and large times.

Affiliated with

Also associated with

No associations

Rating

Time-fractional diffusion of distributed order does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Time-fractional diffusion of distributed order, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-fractional diffusion of distributed order will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369955