On the numerical solutions for the fractional diffusion equation

By Mohamed M. Khader. 2011

335 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9889443c4da35d2866fcae219010fc92b8428bff

How researchers see this paper

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

In Modeling and Simulation

1. Mehdi Dehghan
2. Mehrdad Lakestani
3. S. Irandoust‐pakchin
4. Mohamed M. Khader
5. Mark Ainsworth
6. Ahmed S. Hendy
7. G. Em Karniadakis
8. Nasser Hassan Sweilam

In Numerical Analysis

1. Mehdi Dehghan
2. Mehrdad Lakestani
3. S. Irandoust‐pakchin
4. Mohamed M. Khader
5. Ahmed S. Hendy
6. G. Em Karniadakis
7. Nasser Hassan Sweilam
8. Kevin Burrage

Citations in the corpus

• Numerical studies for the variable-order nonlinear fractional wave equation (2012, methodology): “This method is used to solve many of similar problems to the proposed problem, for example, the variable-order nonlinear cable equation [1], the variable-order nonlinear Stokes’ first problem for a heated generalized second grade fluid [2], the variable-order anomalous sub-diffusion equation [4], th”
• A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “[32] M.M. Khader, On the numerical solutions for the fractional diffusion equation, Commun.”
• Numerical solution of time fractional diffusion systems (2017, background): “On the other hand,it is well known that spectral methods can avoid the discretization of the ’heavy tail’ and are exponentially convergent [23, 26, 41, 45, 46] and so are suitable for non-local problems avoiding the difficulty of using time discretization techniques that need to use all, or most, of”
• Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets (2014, background): “0 x 1, 0< t 1 with initial condition y(x, 0)1⁄4x(2)(1 x) and zero Dirichlet boundary conditions (Khader, 2011).”
• THE APPROXIMATE AND EXACT SOLUTIONS OF THE FRACTIONAL-ORDER DELAY DIFFERENTIAL EQUATIONS USING LEGENDRE SEUDOSPECTRAL METHOD (2012, methodology): “Recently, several approximated methods to solve fractional differential equations have been given such as variational iteration method (see [8], [10]), homotopy perturbation method (see [9], [19], [20]), Adomian’s decomposition method [11], homotopy analysis method [6] and collocation method (see [1”
• Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014, methodology): “Khader [23] proposes a Chebyshev Galerkin method for the discretisation of the fractional diffusion equation where the spatial derivatives are considered in the Caputo sense, similar to the results of Li and Xu [24] for the time-fractional diffusion equation.”