ArticleInternational journal of dynamics and control2023
A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors.
Article in International journal of dynamics and control, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Time delayed fractional diabetes mellitus model and consistent numerical algorithm.Scientific reports · 2024Article
- Navigating climate complexity and its control via hyperchaotic dynamics in a 4D Caputo fractional model.Scientific reports · 2024Article
- Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator.Scientific reports · 2024Article
- A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics.Healthcare analytics (New York, N.Y.) · 2023Article
- A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries.Healthcare analytics (New York, N.Y.) · 2023Article
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Abstract
The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard's theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions
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