On the numerical solutions for the fractional diffusion equation
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Publication:718573
DOI10.1016/j.cnsns.2010.09.007zbMath1221.65263OpenAlexW2057127233MaRDI QIDQ718573
Publication date: 23 September 2011
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cnsns.2010.09.007
Integro-partial differential equations (45K05) Initial-boundary value problems for second-order parabolic equations (35K20) Fractional derivatives and integrals (26A33) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerical studies for a multi-order fractional differential equation
- Homotopy analysis method for fractional IVPs
- Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition
- A second-order accurate numerical method for the two-dimensional fractional diffusion equation
- The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
- An algorithm for the numerical solution of differential equations of fractional order
- Approximate analytical solution for seepage flow with fractional derivatives in porous media
- Finite difference approximations for fractional advection-dispersion flow equations
- Numerical solution of fractional integro-differential equations by collocation method
- Finite difference approximations for two-sided space-fractional partial differential equations
- Discretized Fractional Calculus
- On the Appearance of the Fractional Derivative in the Behavior of Real Materials
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