R language

The article is dedicated to constructing difference approximations of fractal operators in a mathematical model of the impact of chemotherapy on the state of a cancerous tumor, based on fractional calculus using the Caputo derivative. A mathematical model of stem cells and chemotherapy is presented. Numerical algorithms for implementing fractional-order mathematical models have been developed using the Atangana-Toufik method. The UML diagram of the software application and its development process are described.

This paper explores the application of the ARFIMA fractal model for prediction of the dynamics of river water pollution based on BOD measure. The study begins by conducting a review of related works in the field of water quality analysis. At this stage also a suitable dataset is selected, that is used to train the ARFIMA, one of the machine learning models. GPH semi-parametric algorithm is applied for estimating the fractal differentiation parameter of the ARFIMA.