Lithium-ion batteries have emerged as the state-of-the-art energy storage for portable electronics, electrified vehicles, and smart grids. An enabling Battery Management System holds the key for efficient and reliable system operation, in which State-of-Charge (SOC) estimation and State-of-Health (SOH) monitoring are of particular importance. In this paper, an SOC and SOH co-estimation scheme is proposed based on the fractional-order calculus. First, a fractional-order equivalent circuit model is established and parameterized using a Hybrid Genetic Algorithm/Particle Swarm Optimization method. This model is capable of predicting the voltage response with a root-mean-squared error less than 10 mV under various driving-cycle-based tests. Comparative studies show that it improves the modeling accuracy appreciably from its second- and third-order counterparts. Then, a dual fractional-order extended Kalman filter is put forward to realize simultaneous SOC and SOH estimation. Extensive experimental results show that the maximum steady-state errors of SOC and SOH estimation can be achieved within 1%, in the presence of initial deviation, noise, and disturbance. The resilience of the co-estimation scheme against battery aging is also verified through experimentation.