Modified 5-point fractional formula with Richardson extrapolation

Abstract

In this paper, we establish a novel fractional numerical modification of the 5-point classical central formula; called the modified 5-point fractional formula for approximating the first fractional-order derivative in the sense of the Caputo operator. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

Keywords

• richardson extrapolation
• riemann-liouville fractional derivative and integral
• lagrange interpolating polynomial
• caputo derivative