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. The impact of fractal characteristics (long-term memory) of chemotherapy on the state of a cancerous tumor is analysed. The presence of a fractional-order time derivative as a parameter of the solutions provides important information for predicting the effects of chemotherapy on the tumor's state.
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