<p>Fractional-order memristive devices are of interest, as they possess the possibility to mimic certain functions found in biological information processing. Previous research proposed an approach to energy-efficient programming of fractional-order memristive devices based on the use of one or two pulses. We enhance this methodology by generalizing it to accommodate any number of pulses, including the limit of a continuous waveform. In addition, we explore the case of repeated switching to gain a deeper understanding of how devices behave under continuous programming conditions. In this case, we find that the Joule losses per cycle slowly decrease, approaching a limit as the number of past cycles increases. Integrating our methods into real circuit designs will be particularly important for low-power applications. We hope that our findings may be useful for developing nature-inspired, efficient, and highly parallel data processing architectures.</p>