Approximate solution of multi-term fractional differential equations via a block-by-block method

In this paper we introduce a block-by-block method for the numerical solution of multi-term fractional differential equations (MFDEs). The main idea is to convert a MFDE to a Volterra integral equation of weakly singular type, to which a well known block-by-block method is applied. We also provide the error analysis and convergence of the method. Finally, numerical examples involving Bagley-Torvik and relaxation-oscillation equations are given to confirm applications and the theoretical results.