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
Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials
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A unified spectral method for FPDEs with two-sided derivatives; part I: A fast solver
TL;DR: In this article, a unified Petrov-Galerkin spectral method was developed for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form D t 2 τ 0 u + ∑ i = 1 d [ c l i a i D x i 2 μ i u + c r i x i D b i 2 ν j u ] + γ u = ∑ j
Fractional operator method on a multi-mutation and intrinsic resistance model
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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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