Explicit numerical schemes for fractional partial differential equations.
The paper "Algorithms for the fractional calculus: A selection of numerical methods" by Diethelm et al (2005) in Computer methods in applied mechanics and engineering, vol 194, pp 743-773 gives a very good review. In the paper's own words, it gives the newcomer "the necessary tools required to work with fractional models in an efficient way" --- this paper would be a good place to start...good luck
A new book by D. Baleanu, K. Diethelem, E. Scalas and JJ. Trujillo "Fractional Calculus: Models and Numerical Methods. Vol. 3. World Scientific, 2012 contains a complete survey (Chapter 3.2)
We have recently published a paper on efficient diagonal solvers for reaction-diffusion systems described by the fractional Laplacian, including easy-to-code examples. It can be found at:
https://www.researchgate.net/publication/260594928_Fourier_spectral_methods_for_fractional-in-space_reaction-diffusion_equations
or
http://link.springer.com/article/10.1007%2Fs10543-014-0484-2
Article Fourier spectral methods for fractional-in-space reaction-di...
The answer to this question is also important to me, thank you very much for your quastion...
Dear Ali,
Refer the following:
"Fractional Calculus: Models and Numerical Methods" by D. Baleanu, K. Diethelem, E. Scalas and JJ. Trujillo, Vol. 3. World Scientific, 2012 (See, Chapter 3.2)
Explicit methods for fractional differential equations and their stability properties by LucianoGaleone and RobertoGarrappa, Journal of Computational and Applied Mathematics, Volume 228, Issue 2, 15 June 2009, Pages 548-560.
"Algorithms for the fractional calculus: A selection of numerical methods" by Diethelm et al in Computer Methods in Applied Mechanics and Engineering, 194(2005) , 743-773.
Numerical methods for fractional partial differential equations by Changpin Li and An Chen , International Journal of Computer Mathematics, (2017)95:6-7, 1048-1099, DOI: 10.1080/00207160.2017.1343941.
FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS by CHANGPIN LI and FANHAI ZENG, International Journal of Bifurcation and Chaos, 2012, 22:04
Dear collegue
You can use the following books:
1- Numerical Solution of Fractional Order Differential Equations by extrapolation, Kai Diethelm and Guido Walz
2- Intelligent Numerical Methods: Applications to Fractional Calculus by George A. Anastassiou and Ioannis K. Argyros
You can read the Chapter 3 from the following book:
D. Baleanu, K. Diethelem, E. Scalas and JJ. Trujillo, Fractional Calculus: Models and Numerical Methods , Vol. 3. World Scientific, (2012) .
See attached papers maybe help you:
https://arxiv.org/ftp/arxiv/papers/1712/1712.09207.pdf
https://www.tandfonline.com/doi/abs/10.1080/00207160.2017.1343941?src=recsys&journalCode=gcom20
Article Numerical methods for the solution of partial difierential e...
You can find a lot in works of prof. J. Leszczynski: https://www.researchgate.net/scientific-contributions/10754605_Jacek_Leszczynski
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