Background/Objectives: In the modern healthcare landscape, breast cancer remains one of the most prevalent malignancies and a leading cause of mortality among women worldwide. Early and accurate prediction of breast cancer plays a pivotal role in effective diagnosis, treatment planning, and improving survival outcomes. However, due to the complexity and heterogeneity of medical data, achieving high predictive accuracy remains a significant challenge. This study proposes an intelligent hybrid system that integrates traditional machine learning (ML), deep learning (DL), and ensemble learning approaches for enhanced breast cancer prediction using the Wisconsin Breast Cancer Dataset. Methods: The proposed system employs a multistage framework comprising three main phases: (1) data preprocessing and balancing, which involves normalization using the min–max technique and application of the Synthetic Minority Over-sampling Technique (SMOTE) to mitigate class imbalance; (2) model development, where multiple ML algorithms, DL architectures, and a novel ensemble model are applied to the preprocessed data; and (3) model evaluation and validation, performed under three distinct training–testing scenarios to ensure robustness and generalizability. Model performance was assessed using six statistical evaluation metrics—accuracy, precision, recall, F1-score, specificity, and AUC—alongside graphical analyses and rigorous statistical tests to evaluate predictive consistency. Results: The findings demonstrate that the proposed ensemble model significantly outperforms individual machine learning and deep learning models in terms of predictive accuracy, stability, and reliability. A comparative analysis also reveals that the ensemble system surpasses several state-of-the-art methods reported in the literature. Conclusions: The proposed intelligent hybrid system offers a promising, multidisciplinary approach for improving diagnostic decision support in breast cancer prediction. By integrating advanced data preprocessing, machine learning, and deep learning paradigms within a unified ensemble framework, this study contributes to the broader goals of precision oncology and AI-driven healthcare, aligning with global efforts to enhance early cancer detection and personalized medical care.

This study introduces a new class of coupled differential systems described by fractal–fractional Caputo derivatives with both constant and state-dependent delays. In contrast to traditional delay differential equations, the proposed framework integrates memory effects and geometric complexity while capturing adaptive feedback delays that vary with the system’s state. Such a formulation provides a closer representation of biological and physical processes in which delays are not fixed but evolve dynamically. Sufficient conditions for the existence and uniqueness of solutions are established using fixed-point theory, while the stability of the solution is investigated via the Hyers–Ulam (HU) stability approach. To demonstrate applicability, the approach is applied to two illustrative examples, including a predator–prey interaction model. The findings advance the theory of fractional-order systems with mixed delays and offer a rigorous foundation for developing realistic, application-driven dynamical models.

This study introduces a novel Fuzzy Piecewise Fractional Derivative (FPFD) framework to enhance epidemiological modeling, specifically for the multi-phasic co-infection dynamics of Omicron and malaria. We address the limitations of traditional models by incorporating two key realities. First, we use fuzzy set theory to manage the inherent uncertainty in biological parameters. Second, we employ piecewise fractional operators to capture the dynamic, phase-dependent nature of epidemics. The framework utilizes a fuzzy classical derivative for initial memoryless spread and transitions to a fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivative to capture post-intervention memory effects. We establish the mathematical rigor of the FPFD model through proofs of positivity, boundedness, and stability of equilibrium points, including the basic reproductive number (R0). A hybrid numerical scheme, combining Fuzzy Runge–Kutta and Fuzzy Fractional Adams–Bashforth–Moulton algorithms, is developed for solving the system. Simulations show that the framework successfully models dynamic shifts while propagating uncertainty. This provides forecasts that are more robust and practical, directly informing public health interventions.

Polycystic Ovary Syndrome (PCOS) is a widespread hormonal disorder affecting women of reproductive age, often leading to infertility and associated complications. This study presents a comprehensive stochastic mathematical framework to analyze the dynamics of PCOS with a particular focus on infertility and treatment outcomes. Here, the transitions between compartments represent progression of women through clinical states of PCOS (risk, diagnosis, treatment, recovery) rather than infection or transmission, since PCOS is a non-communicable disorder. The model incorporates probabilistic elements to break the symmetric and predictable assumptions inherent in deterministic approaches. This allows it to reflect the randomness and asymmetry in hormonal regulation and ovulation cycles, enabling a more realistic representation of disease progression. By utilizing stochastic differential equations, the study evaluates the impact of treatment adherence on fertility restoration. We establish the conditions for disease extinction versus the existence of an ergodic stationary distribution, which represents a form of long-term statistical symmetry. The results emphasize the importance of early diagnosis and consistent treatment. Furthermore, the proposed approach provides a valuable tool for clinicians to predict patient-specific trajectories and optimize individualized treatment plans, accounting for the asymmetric nature of patient responses.