Finite difference approximations for fractional advection-dispersion flow equations
TL;DR: In this paper, the authors developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain and demonstrated the practical application of these results is illustrated by modeling a radial flow problem.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 Nov 2004. and is currently open access. The article focuses on the topics: Fractional calculus & Finite difference.
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Citations
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A Finite Difference Method on Quasi-uniform Mesh for Time-Fractional Advection-Diffusion Equations with Source Term.
TL;DR: In this paper, the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform grids is discussed.
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Approximate solutions for the fractional advection–dispersion equation using Legendre pseudo-spectral method
TL;DR: In this paper, an efficient numerical method for fractional advection-dispersion equation (FADE) based on Legendre polynomials is proposed to solve FADE.
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High order difference schemes for a time fractional differential equation with Neumann boundary conditions
Seakweng Vong,Zhibo Wang +1 more
TL;DR: A compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions and a high order alternating direction implicit (ADI) scheme is also constructed for the two-dimensional case.
20
Finite element approximation of fractional order elliptic boundary value problems
Béla J. Szekeres,Ferenc Izsák +1 more
TL;DR: It is proved that this approach, which is also called the matrix transformation or matrix transfer method, delivers optimal rate of convergence in the L 2 -norm.
20
Log orthogonal functions: approximation properties and applications
Sheng Chen,Jie Shen +1 more
TL;DR: In this article, two new classes of orthogonal functions, generalized log orthogonality (GLOFs) and generalized Laguerre polynomials (GLO), were proposed.
19
References
•Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
- 19 May 1993
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
•Book
Fractional Integrals and Derivatives: Theory and Applications
Stefan Samko,Anatoly A. Kilbas,O. I. Marichev +2 more
- 08 Dec 1993
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.
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