Comparison of Fractional-Order and Integer-Order Cancer Tumor Growth Models: An Inverse Approach

Abstract

Mathematical modelling of real world phenomena via integer-order differential equation (DE) models has been a popular topic of research for decades. A wide variety of articles have been written in this area and major advancements in model accuracy have been made. Some recent research suggests that fractional-order DEs may more accurately model real world phenomena compared to integer-order counterparts. The development of solution techniques to fractional DEs have been proposed in a number of recent articles. In this paper, we compare fractional-order and integer-order DE models for fitting cancer patient data for tumor growth using fractional DE models. Utilizing actual patient data, we modify three existing integer-order models by instead treating the order of the DE as an unknown parameter. Using a collage-coding inverse problem technique, the order of the DE as well as other parameters in the model are recovered. Finally, results are compared.