Physical Sciences and Mathematics Commons^™

Monte Carlo Random Walk Simulations Based On Distributed Order Differential Equations With Applications In Cell Biology, Erik Andries, Sabir Umarov, Stanly Steinberg

Mathematics Faculty Publications

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved. Simulations based upon multi-term fractional order differential equations are performed.