In this paper we attack the challenging problem of modeling subdiffusion with an arbitrary space-time-dependent driving. Our method is based on a combination of the Langevin-type dynamics with subordination techniques. For the case of a purely time-dependent force, we recover the death of linear response and field-induced dispersion -- two significant physical properties well-known from the stu...

Electron beam dose calculations are often based on pencil beam formulas such as the Fermi-Eyges formula. The Fermi-Eyges formula gives an exact solution of the Fermi equation. The Fermi equation can be derived from a more fundamental mathematical model, the linear Boltzmann equation, in two steps. First, the linear Boltzmann equation is approximated by the Fokker-Planck equation. Second, the Fo...

Anomalous diffusion processes are ubiquitous in biology and arise in the transport of proteins, vesicles and other particles. Such anomalously diffusive behavior is attributed to a number of factors within the cell including heterogeneous environments, active transport processes and local trapping/binding. There are a number of microscopic principles—such as power law jump size and/or waiting t...

This study used the Daftardar-Jafari approach to find approximate and analytical solution for Fokker-Planck (F-P) equation with operator Caputo-Fabrizio (DJM). The accuracy, efficiency, simplicity of current technique are excellent.

An approach to random processes with memory based on a fractal generalization of the Fokker-Planck-Kolmogorov equation in which the fractal time derivative describes what part of the system states is losed, and the other is conserved for all time of evolution is analyzed. It is shown that in the simple case of the fractional time diffusion-wave equation there are self-organization processes con...

We have significant accomplishments on uncertainty quantification in inverse problems for dynamical systems, generalized sensitivity and optimal design of experiments, elasticity and viscoelasticity modeling for buried target detection, and general inverse problem methodology for proliferating populations. Our efforts have continued on development of efficient accurate integration of Fokker Pla...

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise...

Physical and chemical stochastic processes described by the master equation are investigated. The system-size expansion, called the Ω-expansion, trasnforms the master equation to the corresponding Fokker-Planck equation. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master equation, the exact expression of...