Iterative Bernstein splines technique applied to fractional order differential equations

Abstract

<p style='text-indent:20px;'>In this work we will discuss about an approximation method for initial value problems associated to fractional order differential equations. For this method we will use Bernstein spline approximation in combination with the Banach's Fixed Point Theorem. In order to illustrate our results, some numerical examples will be presented at the end of this article.</p>

A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations

“…Lubich [33] on the other hand deals with singularities by introducing certain correction terms. Other approaches have been considered such as Adams methods [21], trapezoidal methods [23] and Bernstein splines [38] while Garrappa [24] has given a survey and software tutorial on numerical methods for FDEs.…”