Theoretical analysis of colonic crypt and colorectal cancer model through Caputo–Fabrizio fractional derivative

Abstract

This study aims to analyze the solution of a system of differential equations that describes the mathematical modeling of cell population dynamics in colonic crypt and colorectal cancer. The Caputo–Fabrizio fractional order derivatives are used to fractionalize the model. The corresponding mathematical model is solved by the Laplace transform, which helps transform differential equations into terms of algebraic equations. The Partial fraction technique is used to find the inverse Laplace of the governing equations. To assess the credibility of the results, graphical simulation has been investigated by manipulating certain parameters. There is a special scenario, namely when $\alpha \to 1$, where the solutions obtained align with those already documented in the literature. This alignment ensures that the initial conditions are met and confirms the accuracy of our solutions.