In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.

翻译：本文研究分数阶微分方程的数值求解问题。具体而言，我们提出了一种基于标准正交雅可比多项式展开向量场的逐级渐变网格方法。在适当宽松的假设条件下，该方法能够实现谱精度。通过若干数值算例验证了理论分析结果。