Boundary value problems for fractional diffusion equations

By Ralf Metzler, Joseph Klafter. 2000

481 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e8c7f7330b8a1faa92487267f8063704f2b192ad

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Weighted average finite difference methods for fractional diffusion equations (2004, unknown): “There are many analytical techniques for dealing with these fractional equations [3,4, 13 ].”
Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation (2013, methodology): “For a well-posedness analysis, we refer to [10, 13, 14, 31, 32, 35, 43].”
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration (2010, background): “See also Metzler, Glöckle and Nonnenmacher [32], Metzler and Klafter [33], Roman [43].”
An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations (2003, unknown): “Some exact analytical solutions for a few cases, although important, are already known in terms of special functions such as the Wright function and Fox’s Hfunction [6, 7, 15, 16].”
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “The MFPT diverges both in the absence of a bias and under a constant drift, pertaining to both finite as well as semi-infinite domains (Metzler and Klafter 2000e, Rangarajan and Ding 2000a, 2000b, 2003, Scher et al 2002a, Barkai 2001)22.”
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation (2011, background): “to [1], [6], [8], [21], [23], [25] to mention only few of many recent publications.”
A fully discrete difference scheme for a diffusion-wave system (2006, methodology): “[17] R. Metzler, J. Klafter, Boundary value problems for fractional diffusion equations, Physica A 278 (2000) 107–125.”
An inverse time-dependent source problem for a time-fractional diffusion equation (2016, unknown): “For the last few decades, fractional diffusion equations have attracted great attention not only from mathematicians and engineers but also from many scientists from fields like biology, physics, chemistry and biochemistry, medicine and finance [9, 17, 18, 26, 45, 46].”
Variational iteration method for fractional heat- and wave-like equations (2009, background): “(1) reduce to the fractional wave-like equation which models anomalous diffusive and subdiffusive systems, description of fractional random walk, unification of diffusion and wave propagation phenomena [40] [41] [42] [43].”
Hamiltonian formulation of systems with linear velocities within Riemann–Liouville fractional derivatives (2005, methodology): “Fractional derivatives were applied in recent studies of scaling phenomena [ 10-12 ].”
An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients (2015, background): “The fractional differential equations have an another important issue in the probability theory related to non-Markovian diffusion processes with a memory (see [26, 27]).”
Boundary value problems for multi-term fractional differential equations (2008, methodology): “Agrawal [11] has solved fractional diffusion equation using finite sine transform method, and Metzler and Klafter [6] have employed the method of images and Fourier–Laplace transform.”
Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain (2002, methodology): “Recently, Metzler and Klafter [ 17 ] used the method of images and the Fourier-transform techniques to solve a fractional diffusion equation for absorbing and reflecting boundary conditions.”