JSPR-Net: A Jacobian-stabilized physics-informed residual neural network for breast cancer detection and fractional-order disease progression modeling.

Breast cancer is the second most common cause of mortality in women. The oncogenes are present in the cells. The milk gland has irregular meiosis and mitosis cell division and cause tumors structure that known as Breast cancer.This study proposes the JSPR-Net classifier for the detection of breast cancer. The detection framework for a new fractional-order compartmental model that uses CF derivatives captures the dynamics of breast cancer progression that depend on memory across different stages of the disease. Fixed-point theory for existence and uniqueness and Natural transform with Ulam-Hyers stability make sure that the model's math is solid and that the numbers are reliable. Graphical visualizations reveal significant disease dynamic variations under different fractional orders (α=0.7,0.8,0.9,1.0), while equilibrium analysis provides insights for intervention strategies and CF method for progress identification of Breast cancer. The kaggle dataset with 250 samples for disease detection is used. The diagnosis accuracy 94% is achieved by proposed method. The achieved accuracy, feature importance and stability analysis shows the robustness of model for breast cancer detection.