Abstract We consider the Dirichlet boundary value problem for linear fractional differential equations with the Riemann–Liouville fractional derivatives. By transforming the boundary value problem to the integral equation, some regularity properties of the exact solution are derived. Based on these properties, the numerical solution of the boundary value problems by a grid method is discussed and weighted estimates considering the boundary effect are obtained. It is shown that the accuracy (the convergence rate) near the boundary is better than inside the domain due to the influence of the Dirichlet boundary condition.

中文翻译：

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带分数导数的边界值问题的加权估计

摘要 我们考虑具有黎曼-刘维尔分数阶导数的线性分数阶微分方程的狄利克雷边值问题。通过将边值问题转化为积分方程，推导出了精确解的一些正则性。基于这些性质，讨论了网格法对边值问题的数值解，得到了考虑边界效应的加权估计。结果表明，由于狄利克雷边界条件的影响，边界附近的精度（收敛速度）优于域内。