A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method

摘要

In this note, two numerical methods of solving fractional differentialequations (FDEs) are briefly described, namely predictor-corrector approach ofAdams-Bashforth-Moulton type and multi-step generalized differential transformmethod (MSGDTM), and then a demonstrating example is given to compare theresults of the methods. It is shown that the MSGDTM, which is an enhancement ofthe generalized differential transform method, neglects the effect of non-localstructure of fractional differentiation operators and fails to accurately solvethe FDEs over large domains.