For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we demonstrate that the so-called proportional secting technique for selecting the required initial values leads to numerical schemes that converge to high accuracy in a very small number of shooting iterations, and we provide an explanation of the analytical background for this favourable numerical behaviour.

翻译：针对使用Caputo导数的阶数 $\alpha \in (1,2)$ 非线性分数阶微分方程对应的Dirichlet型边值问题的数值求解，我们建议采用打靶法。具体而言，我们证明了所谓比例分割技术在选择所需初值时，能够使得数值格式在极少的打靶迭代次数内收敛到高精度，并对这一有利数值行为给出了分析层面的解释。