Uniform approximation of fractional derivatives and integrals with application to fractional differential equations

Abstract

It is well known that for every f ε Cm there exists a polynomial pn such that pn (k) → f(k), k = 0,..m,Here we prove such a result for fractional (non-integer) derivatives. Moreover, a numerical method is proposed for fractional differential equations. The convergence rate and stability of the proposed method are obtained. Illustrative examples are discussed.