Generalised Diffusion and Wave Equations: Recent Advances
Statistical Mechanics
2019-03-05 v1 Mathematical Physics
math.MP
Abstract
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional, distributed order, and tempered time-fractional diffusion and wave equations. Such equations exhibit multi-scaling time behaviour, which makes them suitable for the description of different diffusive regimes and characteristic crossover dynamics in complex systems.
Cite
@article{arxiv.1903.01166,
title = {Generalised Diffusion and Wave Equations: Recent Advances},
author = {Trifce Sandev and Ralf Metzler and Aleksei Chechkin},
journal= {arXiv preprint arXiv:1903.01166},
year = {2019}
}