<p>We present a quantum-inspired computational framework for parameter estimation in fractional ordinary differential equations, addressing the persistent challenge of determining the fractional order from noisy experimental observations. The inverse problem presents fundamental computational difficulties including non-convex objective landscapes with multiple local minima, expensive forward problem evaluations, and high sensitivity to measurement noise. Our approach integrates discrete quantum state encoding of the parameter space with Hamiltonian energy formulation, simulated quantum annealing employing adaptive tunneling mechanisms for global exploration, and variational quantum refinement achieving continuous sub-resolution accuracy. The quantum tunneling mechanism enables escape from spurious local minima that trap conventional gradient-based optimizers, while the hybrid quantum-classical architecture balances computational efficiency with precision. Comprehensive numerical experiments on canonical test problems—the linear fractional relaxation equation and the nonlinear fractional logistic equation—demonstrate robust performance under realistic noise conditions across extensive Monte Carlo trials. Comparative benchmarking against standard optimization techniques including gradient descent, classical simulated annealing, particle swarm optimization, and genetic algorithms reveals substantial advantages in both reliability and computational efficiency. The quantum-inspired method achieves sub-percent accuracy with high success rates while requiring significantly fewer function evaluations than classical metaheuristics. This work establishes both theoretical foundations and practical algorithms for applying quantum computing principles to inverse problems in fractional calculus, providing a pathway toward quantum advantage as hardware capabilities mature.</p>