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：针对基于Caputo导数、阶数$\alpha \in (1,2)$的非线性分数阶微分方程相关的Dirichlet型边值问题的数值求解，我们提出采用射击法。特别地，我们证明了通过所谓的比例割线法选取所需初值，能使数值格式在极少的射击迭代次数内收敛至高精度，并为此优异数值行为提供了分析背景的解释。