<p>Fractional-order models capture memory and hereditary effects that cannot be represented by classical differential equations, yet their non-local nature makes associated optimal control problems computationally demanding. We propose a framework for solving fractional optimal control problems (FOCPs) by synergizing hybrid Hermite and Block-pulse functions with operational matrix techniques. The proposed methodology constructs a hybrid basis that combines the spectral accuracy of Hermite polynomials with the temporal localization of Block-pulse functions, enabling efficient discretization of fractional order dynamics. We derive rigorous operational matrices for Riemann-Liouville fractional integration and multiplication within this hybrid framework. A thorough convergence analysis shows exponential local and algebraic global error decay. These matrices transform FOCPs into purely algebraic optimization problems through generalized Lagrange multipliers, effectively handling both Caputo derivatives and non-smooth control inputs. Numerical case studies illustrate the method’s applicability to nonlinear FOCPs, demonstrating competitive computational accuracy compared to existing approaches.</p>