In this paper, we consider two accurate iterative methods for solving fractional differential equations with power law and Mittag–Leffler kernel. We focused our attention on the stage-structured prey–predator model and several chaotic attractors of type Newton–Leipnik, Rabinovich–Fabrikant, Dadras, Aizawa, Thomas’ and 4 wings. The first algorithm is based on the trapezoidal product-integration rule, and the second one is based on Lagrange interpolations. The results obtained show that both numerical methods are very efficient and provide precise and outstanding results to determine approximate numerical solutions of fractional differential equations with non-local singular kernels.

中文翻译：

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使用 Mittag-Leffler 记忆模拟动力系统和捕捉混沌行为的两种有效数值方案

在本文中，我们考虑使用幂律和 Mittag-Leffler 核求解分数阶微分方程的两种精确迭代方法。我们将注意力集中在阶段结构的猎物-捕食者模型和 Newton-Leipnik、Rabinovich-Fabrikant、Dadras、Aizawa、Thomas 和 4 翼类型的几个混沌吸引子上。第一种算法基于梯形积积分规则，第二种算法基于拉格朗日插值。得到的结果表明，这两种数值方法都非常有效，并且为确定具有非局部奇异核的分数阶微分方程的近似数值解提供了精确和出色的结果。