Open Access

ARTICLE

A Hybrid Machine Learning and Fractional-Order Dynamical Framework for Multi-Scale Prediction of Breast Cancer Progression

David Amilo^1,*, Khadijeh Sadri¹, Evren Hincal^1,2, Mohamed Hafez^3,4

1 Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia, 99138, Turkey
2 Research Center of Applied Mathematics, Khazar University, Baku, AZ1096, Azerbaijan
3 Department of Civil Engineering, Faculty of Engineering, FEQS INTI-IU, University, Nilai, 71800, Malaysia
4 Faculty of Management, Shinawatra University, Pathum, 12160, Thani, Thailand

* Corresponding Author: David Amilo. Email:

(This article belongs to the Special Issue: Innovative Applications of Fractional Modeling and AI for Real-World Problems)

Computer Modeling in Engineering & Sciences 2025, 145(2), 2189-2222. https://doi.org/10.32604/cmes.2025.070298

Received 12 July 2025; Accepted 04 September 2025; Issue published 26 November 2025

Abstract

Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction. We present a hybrid framework that integrates machine learning (ML) and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales. On the Wisconsin Diagnostic Breast Cancer dataset, seven ML algorithms were evaluated, with deep neural networks (DNNs) achieving the highest accuracy (97.72%). Key morphological features (area, radius, texture, and concavity) were identified as top malignancy predictors, aligning with clinical intuition. Beyond static classification, we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression. The model revealed clinically interpretable patterns: lower fractional orders correlated with prolonged aggressive growth, while higher orders indicated rapid stabilization, mimicking indolent subtypes. Theoretical analyses were rigorously proven, and numerical simulations closely fit clinical data. The framework’s clinical utility is demonstrated through an interactive graphics user interface (GUI) that integrates real-time risk assessment with growth trajectory simulations.

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Keywords

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