On the construction of finite-term recursions for Fractional Differential Equations

This paper deals with the numerical solution of Fractional Differential Equations by means of m-step recursions. For the construction of such formulas, we consider a technique based on a rational approximation of the generating functions of Fractional Backward Differentiation Formulas (FBDFs). The so-defined methods simulate very well the properties of the underlying FBDFs with noticeable advantages in terms of memory saving. This fact becomes particularly evident when they are used for discretizing fractional partial differential equations like the ones occurring in some population dynamic models