Numerical simulation of time-fractional diffusion-wave processes applied to communication in bacterial populations

The paper proposes a time-fractional diffusion-wave modification of the bacterial communication model to explore different dynamical regimes of the biological system. The model is formalized as an initialboundary value problem for a system of partial differential equations with Caputo time-fractional derivatives. A finite-difference implicit scheme coupled with an iterative procedure is constructed to solve the problem numerically. Computational experiments indicate realistic time-dependent fluctuations of signal compounds corresponding to the superdiffusion mode.