Related papers: Application of Fractional Derivative Operators to …
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
We show that the anomalous diffusion equations with a fractional derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the L\'evy stable distributions which stem from the evolution properties…
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…
A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown,…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional…
We study the existence of global weak solutions of a nonlinear transport-diffusion equation with a fractional derivative in the time variable and under some extra hypotheses, we also study some regularity properties for this type of…
We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…
We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
We demonstrate that the Fokker-Planck equation can be generalized into a 'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions…