Ultracapacitors (UCs) have been widely recognized as an enabling energy storage technology in various industrial applications. They hold several advantages including high power density and exceptionally long lifespan over the well-adopted battery technology. Accurate modeling and State-of-Charge (SOC) estimation of UCs are essential for reliability, resilience, and safety in UC-powered system operations. In this paper, a novel fractional-order model composed of a series resistor, a constant-phase-element (CPE), and a Walburg-like element, is proposed to emulate the UC dynamics. The Grünald-Letnikov derivative (GLD) is then employed to discretize the continuous-time fractional-order model. The model parameters are optimally extracted using genetic algorithm (GA), based on the time-domain data acquired through the Federal Urban Driving Schedule (FUDS) test. By means of this fractional-order model, a fractional Kalman filter is synthesized to recursively estimate the UC SOC. Validation results prove that the proposed fractional-order modeling and state estimation scheme is accurate and outperforms current practice based on integer-order techniques.