In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the derivative is different from one. A simplified way of constructing the Riemann-Liouville (R-L) fractional operators, fractional integral and fractional derivative, is presented along with examples of its application on different functions. Furthermore, an introduction to the Aitken's method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, to finally present the results that were obtained when implementing the Aitken's method in the F N-R method.

翻译：在下一份文件中,我们提出了一个方法,以获得分数牛顿-拉夫森(F N-R)方法的趋同顺序,该方法似乎至少具有线性趋同顺序,对于衍生物的顺序不同的情况而言,该方法似乎至少具有线性趋同顺序。我们介绍了建造Riemann-Liouville(R-L)分数操作器的简化方法,即分数集成和分数衍生物,以及该方法适用于不同功能的实例。此外,还介绍了Aitken方法的导言,并解释了为什么它有能力加速迭接方法的趋同,最后介绍在F N-R方法中实施Aitken方法时所取得的成果。