An effective harmony between the exploration and exploitation phases in meta-heuristics is an essential design consideration to provide reliable performance on a wide range of optimization problems. This paper proposes a novel approach to enhance the exploratory behavior of the Harris hawks optimizer (HHO) based on the fractional calculus (FOC) memory concept. In the proposed variant of the HHO, a hawk moves with a fractionalorder velocity, and the rabbit escaping energy is adaptively tuned based on FOC parameters to avoid premature convergence. As a result, the fractional-order modified Harris hawks optimizer (FMHHO) is proposed. The sensitivity of the algorithm performance vis-a-vis the FOC parameters is addressed, and the best variant is recommended based on twenty-three benchmarks. For validating the quality of the proposed variant, twentyeight benchmarks of CEC2017 are tested. For evaluating the proposed variant against the other present-day techniques, several statistical measures and non-parametric tests are performed. Moreover, to demonstrate the applicability of the proposed technique, the proton exchange membrane fuel cell (PEMFC) model parameters estimation process is handled based on several measured datasets. In this series of experiments, the FMHHO variant is compared with the standard HHO and the other techniques based on intensive statistical metrics, mean convergence curves, and dataset fitting. The overall outcome shows that the FOC memory property improves the performance of the classical HHO and leads to accurate and robust solutions fitting the measured data.