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

### Abstract

It is well known that for every $f\in C^m$ there existsÂ a polynomial $p_n$ such that $p^{(k)}_n\rightarrow f^{(k)}$,

$k=0,\ldots,m$. Here we prove such a result for fractional

(non-integer) derivatives. Moreover, a numerical method is proposed for fractional differential equations. Â The convergence rate and stability of the proposed method Â are obtained. Illustrative examples are discussed.

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Published

2013-11-23

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Articles