A stable numerical algorithm based on support vector regression for fractional initial value problems

Solutions to fractional-order initial value problems are typically non-smooth, which poses challenges for numerical methods. Although the Mittag-Leffler function is well suited to capturing such non-smooth behavior, collocation methods based on it often lead to ill-conditioned systems, resulting in numerical instability. In this letter, we propose a new method for solving fractional-order initial value problems by combining the Mittag-Leffler reproducing kernel function (RKF) with support vector regression.