Optimal control of coupled fractional dynamical systems using Caputo–Fabrizio derivatives and Forward–Backward Sweep Method

Abstract This paper studies the optimal control of coupled dynamical systems governed by Caputo–Fabrizio fractional derivatives, which provide a non-singular memory kernel well-suited for modeling processes with exponentially decaying memory. We derive first-order necessary conditions using a Pontryagin-type maximum principle and develop a numerical algorithm based on the Forward–Backward Sweep Method (FBSM) tailored to the CF operator. The proposed scheme incorporates a stable discretization that accounts for the exponential kernel and provides convergence and error estimates. To demonstrate the effectiveness of the method, numerical experiments are presented that compare the CF formulation with classical and Caputo models, showing smoother control profiles and improved stabilization. These results highlight the advantages of CF-based modeling and the proposed algorithm for the analysis and control of memory-dependent coupled systems.