Hyers–Ulam Stability of Fractal–Fractional Computer Virus Models with the Atangana–Baleanu Operator
Abstract
1. Introduction
2. Preliminar Definitions
3. Model Formulation
4. Boundedness and Non-Negativity of the Solution
5. Existence and Uniqueness
6. Hyers–Ulam Stability
- •
- Hyers–Ulam stability ensures that if the system is subject to small deviations from an approximate solution, there exists a true solution nearby. In other words, small perturbations in the initial conditions do not lead to large deviations in the overall system trajectory, making the model robust to minor errors.
- •
- Lyapunov stability, on the other hand, guarantees that solutions that start close to an equilibrium point remain close over time. It is more focused on maintaining system stability around equilibrium states rather than ensuring proximity to approximate solutions.
7. Numerical Scheme
8. Numerical Simulation
9. Discussion
10. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Value |
---|---|
0.5 | |
0.5 (VFSS), 0.8 (VPSS) | |
0.001 | |
0.2 | |
0.4 |
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Althubyani, M.; Saber, S. Hyers–Ulam Stability of Fractal–Fractional Computer Virus Models with the Atangana–Baleanu Operator. Fractal Fract. 2025, 9, 158. https://doi.org/10.3390/fractalfract9030158
Althubyani M, Saber S. Hyers–Ulam Stability of Fractal–Fractional Computer Virus Models with the Atangana–Baleanu Operator. Fractal and Fractional. 2025; 9(3):158. https://doi.org/10.3390/fractalfract9030158
Chicago/Turabian StyleAlthubyani, Mohammed, and Sayed Saber. 2025. "Hyers–Ulam Stability of Fractal–Fractional Computer Virus Models with the Atangana–Baleanu Operator" Fractal and Fractional 9, no. 3: 158. https://doi.org/10.3390/fractalfract9030158
APA StyleAlthubyani, M., & Saber, S. (2025). Hyers–Ulam Stability of Fractal–Fractional Computer Virus Models with the Atangana–Baleanu Operator. Fractal and Fractional, 9(3), 158. https://doi.org/10.3390/fractalfract9030158