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 exists a polynomial $p_n$ such that $p_n^{(k)}\to f^{(k)}$, $k=0,\dots ,m$. 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.

This is a preprint of a paper whose final and definite form will appear in Nonlinear Studies, ISSN: 1359-8678 (print) 2153-4373 (online). Paper submitted 12-March-2013; accepted for publication 29-July-2013

References in corpus (2)

• Discrete Direct Methods in the Fractional Calculus of Variations
• Approximation of fractional integrals by means of derivatives

Cited by in corpus (1)

• A Fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives