Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations

The block-by-block method, proposed by Linz for a kind of Volterra integral equations with nonsingular kernels, and extended by Kumarand Agrawal to a class of initial value problems of fractionaldifferential equations (FDEs) with Caputo derivatives, is anefficient and stable scheme. We analytically prove and numericallyverify that this method is convergent with order at least 3 for anyfractional order index $alpha>0$.