Mittag-Leffler RKFs were introduced by Rosenfeld et al. based on the RKFs, a numerical approach called kernelized ABM was developed for solving fractional initial value problems (FIVPs). However, the accuracy of the obtained approximate solution degraded when the fractional order tends to small values. By employing the Mittag-Leffler RKFs, we develop an oversampling collocation technique for Caputo FIVPs with contaminated data. The method can yield higher accurate approximated solution even though the order of the considered FIVPs is small. Also, the approach can improve the numerical instabilities and reduce the influences of noise data.

中文翻译：

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基于Mittag-Leffler核的污染数据分数初值问题过采样配置方法

Mittag-Leffler RKF 由 Rosenfeld 等人提出。基于 RKF，开发了一种称为核化 ABM 的数值方法来解决分数初始值问题 (FIVP)。然而，当分数阶趋于较小值时，所获得的近似解的精度会降低。通过采用 Mittag-Leffler RKF，我们为具有污染数据的 Caputo FIVP 开发了一种过采样搭配技术。即使所考虑的 FIVP 的阶数很小，该方法也可以产生更准确的近似解。此外，该方法还可以改善数值不稳定性并减少噪声数据的影响。