On failed methods of fractional differential equations. The case of multi-step generalized differential transform method
Numerical treatment of fractional differential equations, in a reliable and accurate way, is very challenging in comparison with classical integer-order differential equations. This difficulty is primarily related to the effect of non-local structure of fractional differentiation operators, to the solution of nonlinear equations involved in implicit methods and so forth. In this paper, a so-called method for fractional differential equations (FDEs) is briefly described: the multi-step generalized differential transform method (MSGDTM).