Authors: Ms. Sneha Dattatray Pekhale, Dr. Jatin Majithia
Abstract: Traditional integer-order differential equations are increasingly recognized for their limitations in capturing the non-local, memory-dependent and hereditary properties inherent in complex biological and physical systems. This review provides a comprehensive synthesis of recent research into the application of fractional-order derivatives—including the standard Caputo, Caputo-Fabrizio, Atangana-Baleanu and generalized ψ-Caputo operators—across diverse scientific domains. In epidemiology, these models have proven superior to classical approaches for analyzing the transmission dynamics of diseases such as Tuberculosis, COVID-19 and Dengue fever with some models achieving a 28.6% reduction in predictive error by accounting for specific population behaviors and environmental factors. In oncology, fractional modeling has refined the simulation of radiotherapy and chemotherapy by integrating vital radiobiological factors like cell repair and repopulation, leading to more precise treatment protocols. Beyond medicine, the sources demonstrate the utility of fractional calculus in modeling ecological food chain interactions, world population growth and USA GDP rates as well as optimizing multi-agent systems and gradient descent algorithms. By employing rigorous qualitative analyses (e.g.fixed-point theory) and advanced numerical schemes (e.g.Adams-Bash forth-Moulton method), these studies establish that fractional-order derivatives provide a more flexible and realistic framework for capturing the complexities of real-world phenomena. This review underscores the transformative potential of fractional calculus in enhancing predictive accuracy for public health management and socio-economic forecasting.
DOI: http://doi.org/10.5281/zenodo.20854700
