Well-posedness and Generalized Stability of Caputo Fractional Dynamic Equations on Time Scales with Applications to Epidemiological Models

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DOI: https://doi.org/10.28924/2291-8639-24-2026-233
Published: Aug 3, 2026
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Michael Precious Ineh, Wisdom Kevin Udogworen, Ndianabasi Peter, Julie S. George, Hossam A Nabwey, Reny George, Well-posedness and Generalized Stability of Caputo Fractional Dynamic Equations on Time Scales with Applications to Epidemiological Models, Int. J. Anal. Appl., 24 (2026), 233.

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Michael Precious Ineh, Wisdom Kevin Udogworen, Ndianabasi Peter, Julie S. George, Hossam A Nabwey, Reny George

Abstract

In this work, we extend the theory of fractional calculus to hybrid systems that combine continuous and discrete dynamics by establishing the existence, uniqueness, and generalized Ulam–Hyers–Rassias stability of solutions to Caputo fractional delta-differential equations on time scales. Using the Schauder fixed-point theorem, we derive sufficient conditions for well-posedness and stability, building on core concepts from fractional calculus and time-scale theory. To demonstrate the applicability and practicality of the proposed framework, we apply the theoretical results to epidemiological modelling. In particular, SIS and SIR models are employed to illustrate how the approach captures memory effects and hybrid dynamics inherent in real-world systems. Thus, the framework not only advances the theoretical foundations of fractional dynamic equations but also highlights their practical relevance.

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