A Gradient-Based Optimization Algorithm for Optimal Control Problems with General Conformable Fractional Derivatives

This paper presents an extended gradient-based optimization framework for optimal control problems governed by general conformable fractional derivatives (GCFDs), which unify various fractional operators and provide greater modeling flexibility than classical conformable derivatives. The proposed study derives necessary optimality conditions for GCFD systems by reformulating the Hamiltonian and adjoint equations to accommodate the general operator. A novel discretization scheme with adaptive collocation points is introduced to efficiently handle kernel-dependent dynamics. Numerical experiments demonstrate the method’s effectiveness, showing up to 20.2% improvement in terminal constraint satisfaction and 11.8% reduction in total cost compared to conformable-only approaches, with similar computational times. Comprehensive comparisons including Caputo derivatives demonstrate 17.8% cost reduction and 40.1% lower terminal state error. Parameter sensitivity analyses further validate kernel selection strategies. Overall, the proposed framework broadens the applicability of gradient-based optimization to a wider class of fractional-order systems, enhancing both performance and flexibility, with future work aimed at convergence analysis and real-world implementation.