Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||33|
|Journal||Fractional Calculus and Applied Analysis|
|Publication status||Published - 1 Aug 2015|
|Publication type||A1 Journal article-refereed|
We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck- Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
- anomalous diffusion, continuous time random walk (CTRW), Fokker- Planck-Smoluchowski equation, Mittag-Leffler functions, multi-scaling