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Zbl 1047.76075
Lynch, V. E.; Carreras, B. A.; del-Castillo-Negrete, D.; Ferreira-Mejias, K. M.; Hicks, H. R.
Numerical methods for the solution of partial differential equations of fractional order.
(English)
[J] J. Comput. Phys. 192, No. 2, 406-421 (2003). ISSN 0021-9991

Summary: Anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas. To model this transport mechanism, fractional order space derivative operators can be used. Here, the numerical properties of partial differential equations of fractional order $\alpha$, $1 \leqslant \alpha \leqslant 2$, are studied. Two numerical schemes, an explicit and a semi-implicit one, are used in solving these equations. Two different discretization methods of the fractional derivative operator have also been used. The accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order.
MSC 2000:
*76M20 Finite difference methods
76X05 Plasmic flows
65R20 Integral equations (numerical methods)

Keywords: Fractional derivatives; Partial differential equations; Anomalous diffusion; Plasma transport

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