Analytical study of a modified-ABC fractional order breast cancer model

This study investigates breast cancer dynamics using modified ABC-fractional operators. We examine interactions among cancer stem cells, tumor cells, healthy cells, excess estrogen effects, and immune cells. By applying the “Localization of Compact Invariant Sets” technique and comparison theory, we establish conditions for cancer persistence without immune cells and eradication with an immune response. We analyze equilibria, global attraction persistence state, stability, solution uniqueness, and existence using recursive sequences and fixed point theorem. Numerical simulations with Lagrange’s interpolation validate and deepen our understanding of breast cancer dynamics. Incorporating modified ABC-fractional derivatives enhances our comprehension of the model.