Time fractional advection-dispersion equation

By Fawang Liu, Vo Anh, Ian L Turner, Pinghui Zhuang. 2003

226 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6c0cdbfcd4d129108982642f4a3cf7c1b353ac59

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Fawang Liu
2. Ian L Turner
3. Chuanju Xu
4. Vo Anh
5. Yumin Lin
6. Pinghui Zhuang
7. Kevin Burrage
8. Yubin Yan

In Modeling and Simulation

1. Fawang Liu
2. Ian L Turner
3. Vo Anh
4. Changpin Li
5. Pinghui Zhuang
6. Kevin Burrage
7. Chuanju Xu
8. Yubin Yan

In Numerical Analysis

1. Fawang Liu
2. Ian L Turner
3. Vo Anh
4. Changpin Li
5. Kevin Burrage
6. Pinghui Zhuang
7. Chuanju Xu
8. Yubin Yan

Citations in the corpus

• Finite difference/spectral approximations for the time-fractional diffusion equation (2007, methodology): “These models have been investigated in analytical and numerical frames by a number of authors [8,11,18,19,21].”
• Fractional high order methods for the nonlinear fractional ordinary differential equation (2007, background): “deal of attention in the last decade [7,15,22–24], especially in the fields of viscoelastic materials [1,10,11,27], electrochemical processes [8], dielectric polarization [28], colored noise [29], anomalous diffusion, signal processing [21], control theory [24], advection and dispersion of solutes i”
• FracFit: A robust parameter estimation tool for fractional calculus models (2017, methodology): “Figure 2 displays the sFADE and TFDE fits for the PSS samples.”
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation (2009, background): “The TFDE as well as the fractional wave equation have been investigated in analytical and numerical frames by a number of authors [9, 17, 30, 39].”
• Implicit difference approximation for the time fractional diffusion equation (2006, background): “Liu et al. [ 10 ] considered time-fractional advection-dispersion equation and derived the complete solution.”
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation (2007, methodology): “[4] considered the time fractional ADE and the solution was obtained using a variable transformation, Mellin and Laplace transforms, and H-functions.”
• Numerical solutions of the space‐time fractional advection‐dispersion equation (2008, unknown): “[7] considered the time fractional advection-dispersion equation and the solution was obtained by using variable transformation, Mellin and Laplace transforms, and properties of H-functions.”
• Numerical solution of the space fractional Fokker-Planck equation (2004, background): “Liu, Anh, Turnar and Zhuang [28] considered time fractional advection-dispersion equation and derived the complete solution.”
• A finite element method for time fractional partial differential equations (2011, methodology): “Analytical solutions of time fractional partial differential equations have been studied using Green’s functions or Fourier-Laplace transforms [26], [23], [30], [33].”
• Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, background): “For example, the TFDE and related equations have been investigated in analytical and numerical frames by a number of authors [14, 26, 45, 54].”