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arXiv · 1308.0451

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

Hassan Khosravian-Arab·Delfim F. M. Torres
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Abstract

It is well known that for every $f\in C^m$ there exists 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. The convergence rate and stability of the proposed method are obtained. Illustrative examples are discussed.

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Hassan Khosravian-Arab, Delfim F. M. Torres. 2013-08-02. Uniform approximation of fractional derivatives and integrals with application to fractional differential equations. https://arxiv.org/abs/1308.0451

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