Mittag-Leffler kernel-based oversampling collocation method for fractional initial value problems with contaminated data

Abstract

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.