Numerical methods for the solution of partial differential equations of fractional order

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 α, 1⩽α⩽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.