Modeling and analysis using piecewise hybrid fractional operator in time scale measure for ebola virus epidemics under Mittag–Leffler kernel

This emerging infectious disease poses one of the most severe threats to public health in these locations, but there are not many reliable therapies yet. In this work, we developed the Ebola virus dynamics and control factors epidemic model with a piecewise hybrid fractional Operator in time scale measure insight of Mittag-Leffler kernel. Patterns and structures that repeat at various scales are the focus of fractal analysis, which has applications in complex systems such as biological ones. Both qualitatively and statistically, a proposed model with the Lipschitz criteria and linear growth is examined, considering positive solutions, boundedness, and uniqueness at equilibrium points with Leray-Schauder results under time scale ideas. The regulation for linear responses approach will be used by Chaos Control to stabilize the system after its equilibrium points. A fractional-order framework with a controlled design will be considered, where solutions are bounded in the feasible domain of relations of different compartments. Ulam-Hyers stability results in the solution are treated when function (constant or rising) for the component of qualitative inquiry in generalized form. The dynamical behaviors of the suggested model are discussed with the Newton polynomial approach used to implement on model in the sense of classical piecewise and Mittag-Leffler kernel at different fractional order values. The model shows that solutions are stable and confined within a feasible range, ensuring reliability. Through detailed simulations, it effectively captures how different interventions and infection rates influence Ebola spread. This fractional-order model enhances understanding of Ebola transmission, providing a strong basis for predicting outbreaks and planning effective control measures, with practical applications for analyzing real-world data.