Related papers: Fractional Derivative Modification of a Drude Mode…
By far, the fractional derivative model is mainly related to the modelling of complicated solid viscoelastic material. In this study, we try to build the fractional derivative PDE model for broadband ultrasound propagation through human…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
In this paper, we study the dynamic formation of transients when plane waves impinge on a dispersive slab that abruptly changes its electrical properties in time. The time-varying slab alternates between air and metal-like states, whose…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
The frequency-dependent attenuation of broadband acoustics is often confronted in many different areas. However, the related time domain simulation is rarely found in literature due to enormous technical difficulty. The currently popular…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
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…
General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the…
The mathematical model of surfactant adsorption under mixed barrier-diffusion control is analyzed using techniques from fractional calculus. The kinetic models of Henry, Langmuir, Frumkin, Volmer and van der Waals are considered. First,…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the…
In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations of order 1 and 2 in time, respectively. By replacing the time…