Fractional motions

II Eliazar, MF Shlesinger - Physics reports, 2013 - Elsevier
Brownian motion is the archetypal model for random transport processes in science and
engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long …

[图书][B] Stochastic models for fractional calculus

MM Meerschaert, A Sikorskii - 2019 - books.google.com
Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

A survey on fractional derivative modeling of power-law frequency-dependent viscous dissipative and scattering attenuation in acoustic wave propagation

W Cai, W Chen, J Fang, S Holm - Applied …, 2018 - asmedigitalcollection.asme.org
This paper aims at presenting a survey of the fractional derivative acoustic wave equations,
which have been developed in recent decades to describe the observed frequency …

A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations

AH Bhrawy, MA Zaky - Journal of Computational Physics, 2015 - Elsevier
In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …

Solution of multi-term time-fractional PDE models arising in mathematical biology and physics by local meshless method

I Ahmad, H Ahmad, P Thounthong, YM Chu… - Symmetry, 2020 - mdpi.com
Fractional differential equations depict nature sufficiently in light of the symmetry properties
which describe biological and physical processes. This article is concerned with the …

Numerical methods for solving the multi-term time-fractional wave-diffusion equation

F Liu, MM Meerschaert, RJ McGough… - Fractional Calculus and …, 2013 - Springer
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The
multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong …

[HTML][HTML] The Galerkin finite element method for a multi-term time-fractional diffusion equation

B Jin, R Lazarov, Y Liu, Z Zhou - Journal of Computational Physics, 2015 - Elsevier
We consider the initial/boundary value problem for a diffusion equation involving multiple
time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space …

Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian

BE Treeby, BT Cox - The Journal of the Acoustical Society of America, 2010 - pubs.aip.org
The efficient simulation of wave propagation through lossy media in which the absorption
follows a frequency power law has many important applications in biomedical ultrasonics …

Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain

H Jiang, F Liu, I Turner, K Burrage - Journal of Mathematical Analysis and …, 2012 - Elsevier
Generalized fractional partial differential equations have now found wide application for
describing important physical phenomena, such as subdiffusive and superdiffusive …

Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

I Ahmad, H Ahmad, M Inc, SW Yao, B Almohsen - Thermal Science, 2020 - doiserbia.nb.rs
In this article, we presented an efficient local meshless method for the numerical treatment of
two term time fractional-order multi-dimensional diffusion PDE. The demand of meshless …