Question
Asked 8 April 2014

Can anyone suggest some articles regarding explicit numerical schemes for fractional order partial differential equations?

Explicit numerical schemes for fractional partial differential equations.

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All Answers (9)

Michael Wendl
Washington University in St. Louis
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
1 Recommendation
Mieczyslaw Cichon
Adam Mickiewicz University in Poznań
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)
1 Recommendation
Alfonso Bueno-Orovio
University of Oxford
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:
or
1 Recommendation
Mehmet Yavuz
Necmettin Erbakan University
The answer to this question is also important to me, thank you very much for your quastion...
2 Recommendations
Boddu Muralee Bala Krushna
Maharaj Vijayaram Gajapathi Raj College of Engineering
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
1 Recommendation
Maamar Benbachir
National Higher School of Mathematics, Scientific and Technology Hub of Sidi Abdellah, P.O. Box 75, Algiers 16093, Algeria.
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
2 Recommendations
Mohammed S. Abdo
Hodeidah University
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) .
2 Recommendations

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