I. Alraddadi - Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia. M. P. Ineh - Department of Mathematics and Computer Science, Ritman University, Ikot Ekpene, Akwa Ibom State, Nigeria. D. K. Igobi - Department of Mathematics, University of Uyo, Uyo, Nigeria. U. Ishtiaq - Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore, Pakistan. I.-L Popa - Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, Alba Iulia 510009, Romania. - Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, Brasov 500091, Romania.
This work introduces a novel analytical framework for analyzing the stability of Caputo fractional dynamic equations on time scales (CFDE\(\mathbb{T}\)) using a two-measure approach combined with comparison principle. By applying paired measures \((m_0, m)\) and vector Lyapunov functions, we derive sufficient conditions for both \((m_0, m)\)-stability and asymptotic stability. The method simplifies analysis by relating the system to a well-understood comparison system, reducing the task to verifying quasimonotonicity and avoiding the need for explicit solutions. The framework’s effectiveness is demonstrated through two biological models, an immune response system and a 3D hypothalamic-pituitary-adrenal (HPA) axis, highlighting its ability to handle nonlinearities, hybrid time scales, and varying system dimensions. This study bridges theoretical stability analysis with practical biomedical applications, advancing the understanding of fractional-order hybrid dynamics.
I. Alraddadi, M. P. Ineh, D. K. Igobi, U. Ishtiaq, I.-L Popa, Stabilization of fractional hybrid systems with applications in biomedical dynamics, Journal of Mathematics and Computer Science, 41 (2026), no. 3, 406--420
Alraddadi I., Ineh M. P., Igobi D. K., Ishtiaq U., Popa I.-L, Stabilization of fractional hybrid systems with applications in biomedical dynamics. J Math Comput SCI-JM. (2026); 41(3):406--420
Alraddadi, I., Ineh, M. P., Igobi, D. K., Ishtiaq, U., Popa, I.-L. "Stabilization of fractional hybrid systems with applications in biomedical dynamics." Journal of Mathematics and Computer Science, 41, no. 3 (2026): 406--420
