相关论文: General Solution of a Fractional Diffusion-Advecti…
In this paper we exactly solve the diffusion-advection equation for cosmic-ray transport. With this purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for this equation. From this solution,…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…
We consider the propagation of galactic cosmic rays under assumption that the interstellar medium is a fractal one. An anomalous diffusion equation in terms of fractional derivatives is used to describe of cosmic ray propagation. The…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…
We consider the propagation of galactic cosmic rays in the fractal interstellar medium. Steady state solution of the fractional diffusion equation, describing cosmic ray propagation, is found. We show that the exponent of the steady state…
We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.
We present an analytic solution to diffusion equation for high energy cosmic rays in the expanding universe. The particles are assumed to be ultra-relativistic and they can have energy losses arbitrarily dependent on energy and time. The…
We consider similarity solutions of the generalized convection-diffusion-reaction equation with both space- and time-dependent convection, diffusion and reaction terms. By introducing the similarity variable, the reaction-diffusion equation…
Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered.…
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 view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
The standard approach to cosmic-ray (CR) propagation in the Galaxy is based on the assumption that local transport properties can be extrapolated to the whole CR confining volume. Such models tend to underestimate the gamma-ray flux above…
Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $\tilde B/\langle B\rangle \sim 1$ is present on top of the mean field gradient,…
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…
A theory of cosmic-ray transport in multi-phase diffusive media is developed, with the specific application to cases in which the cosmic-ray diffusion coefficient has large spatial fluctuations that may be inherently multi-scale. We…