Waveform relaxation methods for fractional differential equations with the Caputo derivatives

In this paper, we report new waveform relaxation methods for fractional differential equations with the Caputo derivatives. The convergence properties of the waveform relaxation methods are studied under linear and nonlinear conditions for the right-hand side of equations. Some convergent splittings are given. This is the first time for studying the waveform relaxation methods for fractional differential equations in references. (C) 2012 Elsevier B.V. All rights reserved.