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In this paper we consider the numerical solution of fractional differential equations by means of m-step recursions. The construction of such formulas can be obtained in many ways.Here we study a technique based on the rational approximation of the generating functions of fractional backward differentiation formulas (FBDFs). Accurate approximations lead to the definition of methods which simulate the underlying FBDF, with important computational advantages. Numerical experiments are presented.

In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix -a special matrix which has only the natural numbers as entries and is closely related to the well known Pascal matrix. By this means we stress the arithmetical origins of Appell polynomials. The approach also allows to derive, in a simplified way, the properties of Appell polynomials by using only matrix operations.