Variation of constant formulas for fractional difference equations

Abstract

Recently, the theory of fractional calculus became very popular and its development is still very fast (see e.g. [22, 25] and the references therein). In the literature, one can find results on theoretical problems as well as practical applications. In the classical framework of differential or difference equations a powerful tool for analyzing properties of dynamical systems is the so-called variation of constant formula which expresses the solution of a nonlinear equation by the solution of a linear approximation and an implicit term involving the nonlinearity