In this paper, we introduce fractional sigmoidal curves and estimate their parameters to fit the given tumor volume data. We outline approximation techniques to choose the appropriate functions of discrete, discrete fractional and continuous fractional calculus. We demonstrate how to replace the exponential function e−ct in the existing continuous time models with these functions. We use the tumor volume data which were taken over consecutive seventeen days, for twenty eight mice.We then compute residual sum of squares, standard error of the estimate, adjusted coefficient of multiple determination, and cross-validation methods to compare models on data fitting and predictive performances. Estrus cycle stages of measurement are also taken into account when comparing the models.
M. Atıcı, Ferhan; Atıcı, Mustafa; J. M. Hrushesky, William; and Nguyen, Ngoc
"Modeling Tumor Volume with Basic Functions of Fractional Calculus,"
Progress in Fractional Differentiation & Applications: Vol. 1
, Article 1.
Available at: https://dc.naturalspublishing.com/pfda/vol1/iss4/1