A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy

Our study is based on the modification of a well-known predator-prey equation, or the Lotka-Volterra competition model. That is, a system of differential equations was established for the population of healthy and cancerous cells within the tumor tissue of a patient struggling with cancer. Besides, fractional differentiation remedies the situation by obtaining a meticulous model with more flexible parameters. Furthermore, a specific type of non-Newtonian calculus, bi-geometric calculus, can describe the model in terms of proportions and implies the alternative aspect of a dynamic system. Moreover, fractional operators in bi-geometric calculus are formulated in terms of Hadamard fractional operators. In this article, the development of fractional operators in non-Newtonian calculus was investigated. The model was extended in these criteria, and the existence and uniqueness of the model were considered and guaranteed in the first step by applying the Arzela-Ascoli. The bi-geometric analogue of the numerical method provided a suitable tool to solve the model approximately. In the end, the visual graphs were obtained by using the MATLAB program.

Automated summary

Our study is based on the modification of the widely known predator-prey equation, the Lotka-Volterra competition model, to investigate the population of healthy and cancerous cells within tumor tissue in cancer patients. We utilize fractional differentiation and bi-geometric calculus to obtain a more flexible model. The Arzela-Ascoli theorem is applied to guarantee the existence and uniqueness of the model, and the bi-geometric analogue of the numerical method provides an effective tool for approximating the solution. The visual graphs generated using MATLAB program further enhance our understanding.