A diffusion model based on a continuous time random walk scheme with a separable transition probability density is introduced. The probability density for long jumps is proportional to x−1−γ (a Lévy-like probability density). Even when the probability density for the walker position at...

We study the relationship between anomalous diffusion and persistent motion of micron-sized particles moving in a viscoelastic environment and subjected to an external noise. In the framework of a generalized Langevin equation, we compare the analytical expressions of the mean square...

In the case of time-fractional diffusion–wave equation considered in the spatial domain −∞x∞, evolution of initial box-signal was investigated by Mainardi [F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996)...

This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we...

We analyse a N-dimensional anisotropic nonlinear Fokker–Planck equation by considering stationary and time-dependent solutions. The stationary solutions are obtained for very general situations, including those when the diffusion coefficients are spatial dependents. Time-dependent solutions...

A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the...

We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂tρ=∂x{D(x)∂μ−1xρν−F(x)ρ} by considering a diffusion coefficient D=D|x|−θ(θ∈R and D0) and a drift force F=−k1x+k̄γx|x|γ−1(k1,k̄γ,γ∈R). Connection with nonextensive...

Generalized transport equations covering both normal transport processes (such as neutron transport) and anomalous ones including Lévy walk and trapping are derived. The behaviours of the spatial distribution and mean-square displacement are investigated for fractal space–time processes....

An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state x as x and |x|α. An exactly soluble model of a system is constructed due to consideration of a specific relation between noises. Exact expressions...

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks)...