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Fractional-Order Nesterov Dynamics for Convex Optimization
Tumelo Ranoto
https://arxiv.org/abs/2509.11987 https://arxiv.org/pdf/2509.11987

Fractional-Order Nesterov Dynamics for Convex Optimization
We propose and analyze a class of second-order dynamical systems for continuous-time optimization that incorporate fractional-order gradient terms. The system is given by \begin{equation} \ddot{x}(t) + \fracα{t}\dot{x}(t) + \nabla^θ f(x(t)) = 0, \end{equation} where $θ\in (1,2)$, and the fractional operators are interpreted in the sense of Caputo, Riemann--Liouville, and Grünwald--Letnikov derivatives. This formulation interpolates between memory effects of fractional dynamics and higher-or…