A Critical Review of Fractional Operators, Control, and Machine Learning in Biomedical Models with Attention to Memory and Identifiability

Fractional operators are used in biomedical balance laws to encode memory. However, the order of the fractional operator used in these models is not the same as the memory recovered from the patients. This review maps one hundred scientific articles from the Scopus and Web of Science databases from 2019 to 2026 in which fractional operators were used in biomedical applications. The articles are separated into three main communities: compartment fractional differential equations, fractional control, and tabular clinical machine learning. For each article, information regarding the fractional operator used, the biomedical plant it acted upon, the type of data used, whether the fractional order was identified, and whether a locked model would change the decision for the clinical application was collected. The results from well-posed Caputo systems, simulated glucose and intraocular-pressure controllers, and fractional physics-informed neural networks were standard results. New methodological pipelines that combined fractional operators with machine learning on public biomedical data tables yielded high area under the curve values and low pseudo-time residuals in predictions, but they have yet to prove whether they recover the fractional order from the biomedical subject’s biological clock. Clinical prediction using these models began only when there was a change in the locked model in an external cohort of biomedical subjects with a biological clock, not when the fractional model was plotted through the public biomedical data tables.