Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments
Abstract
:1. Introduction
2. Preliminaries and Notations
3. The Piecewise Mathematical Model
3.1. Breast Cancer Model Based on Fractal (Fractional and Variable Order) -Caputo Derivative
3.2. Breast Cancer Model Based on Fractal (Fractional and Variable Order) Mittag-Leffler Laws
3.3. The Points of Equilibrium and Their Analysis
4. Numerical Methods for the Proposed Models
4.1. -NSFDM
4.2. NMEMM
Stability of the Proposed Method
- h: The choice of the step size h significantly affects stability. Smaller step sizes generally improve stability but increase computational cost.
- Weights : The stability also depends on the specific form of the weights .
- Function : The function influences the stability through the term . The proper selection of can enhance stability.
4.3. Numerical Method for Crossover Non-Singular Kernel Fractal (Fractional–Variable) Order Models
Toufik–Atangana Method
4.4. NMEMM
5. Numerical Simulations
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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The Variable | Description |
---|---|
Patients with stage one and stage two breast cancer. | |
The group of people with stage three breast cancer. | |
The group of people with stage four breast cancer. | |
Number of breast cancer patients in a state free of the disease. | |
Patients with cardiotoxic breast cancer in the population. |
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Sweilam, N.H.; Al-Mekhlafi, S.M.; Abdel Kareem, W.S.; Alqurishi, G. Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments. Symmetry 2024, 16, 1172. https://doi.org/10.3390/sym16091172
Sweilam NH, Al-Mekhlafi SM, Abdel Kareem WS, Alqurishi G. Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments. Symmetry. 2024; 16(9):1172. https://doi.org/10.3390/sym16091172
Chicago/Turabian StyleSweilam, Nasser H., Seham M. Al-Mekhlafi, Waleed S. Abdel Kareem, and Ghader Alqurishi. 2024. "Comparative Study of Crossover Mathematical Model of Breast Cancer Based on Ψ-Caputo Derivative and Mittag-Leffler Laws: Numerical Treatments" Symmetry 16, no. 9: 1172. https://doi.org/10.3390/sym16091172