论文标题
关于某些分数衍生物的收敛和收敛顺序
About Convergence and Order of Convergence of some Fractional Derivatives
论文作者
论文摘要
在本文中，当分化的顺序接近一个时，我们为Riemann-Liouville，Caputo和Caputo-Fabrizio分数操作员建立了一些融合结果。我们考虑$ \ left | \ left |给出的一些错误d^{1- \ al} f -f'\ right | \ right | _p $ for p = 1和$ p = \ infty $，我们证明，对于Caputo和Caputo Fabrizio操作员，收敛的顺序是正真实的R，0 <r <1。最后，我们比较了Caputo和Caputo-Fabrizio操作员之间的收敛速度，这些速度获得了Digamma函数相关的收敛速度。
In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.
