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This paper proposes a new estimator design algorithm for state-of-charge (SoC) indication of lithium-ion batteries. A fractional-order model-based nonlinear estimator is first framed including a Luenberger term and a sliding mode term. The estimator gains are designed by Lyapunov's direct method, providing a guarantee for stability and robustness of the error system under certain assumptions. This generic estimation algorithm is then applied to lithium-ion batteries. A fractional-order circuit model is adopted to predict battery dynamic behaviours. Assumptions based on which the estimation algorithm is developed are justified and remarked. Experiments corresponding to electric vehicle applications are conducted to parameterize the battery model and demonstrate the estimation performance. It shows that the proposed approach is able to estimate SoC with errors less than 0.03 in the presence of initial deviation …