Abstract

Tumor growth exhibits nonlinear dynamics using driven cellular and microenvironmental heterogeneities. A research study describes a fractional-order model of tumor growth that accounts for memory and hereditary properties as crucial components of tumor dynamics and incorporates targeted therapy. This model accounts for the temporal dependence of tumor growth and the response to therapy. Additionally, nano-particle agents designed for drug delivery serve as distinct perturbations in the tumor growth model. Research integrates tumor cell growth, the quiescent growth model and the addition of drug agents. Research studies indicate that the fractional-order tumor growth model includes quasi-derivatives to capture the nonlocal behavior of tumor growth. Mathematically, growing tumor cell masses individually are not sufficient to account for the model's delay/saturation outcome. Therefore, the tumor cell masses described by the system of nonlinear fractional-order derivatives are also analyzed for existence, uniqueness and stability. We also consider the system's critical points and analyze local stability. Each parameter, including the release rate, targeting, and dosing of the nano-Particles, will be analyzed.  Research founded that the system in this way to fully leverage the various innovative fractional-order solvers. This method captures tumor-drug interactions more accurately and provides substantial insights into the design of targeted cancer therapeutics. In the future, the analysis will be extended to include interactions between the immune response and mechanisms of multidrug resistance for a more holistic, complex therapeutic design.