This article proposes a predictor-corrector scheme for solving the fractional differential equations \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\) with non-uniform meshes. We reduce the fractional differential equation into the Volterra integral equation. Detailed error analysis and stability analysis are investigated. The convergent order of this method on non-uniform meshes is still 3 though \({}_0^C D_t^\alpha y(t)\) is not smooth at \(t=0\). Numerical examples are carried out to verify the theoretical analysis.

中文翻译：

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分数阶微分方程的非均匀网格高阶预测校正方法

本文提出了一种预测校正方案，用于求解非均匀分数阶微分方程 \({}_0^C D_t^\alpha y(t) = f(t,y(t)), \alpha >0\)网格。我们将分数阶微分方程简化为 Volterra 积分方程。研究了详细的误差分析和稳定性分析。尽管 \({}_0^C D_t^\alpha y(t)\) 在 \(t=0\) 处不平滑，但该方法在非均匀网格上的收敛阶数仍然为 3。并通过数值算例验证了理论分析。