Fractional Adams–Moulton methods

In the simulation of dynamical systems exhibiting an ultraslow decay, differential equations of fractional order have been successfully proposed. In this paper we consider the problem of numerically solving fractional differential equations by means of a generalization of k  -step Adams–Moulton multistep methods. Our investigation is focused on stability properties and we determine intervals for the fractional order for which methods are at least A(π/2)A(π/2)-stable. Moreover we prove the A-stable character of k  -step methods for k=0k=0 and k=1k=1.