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Young children frequently die from measles, which is a major global health concern. Despite being more prevalent in infants, pregnant women, and people with compromised immune systems, it can infect anyone. Novel fractional operators, the constant-proportional Caputo operator, and the constant-proportional Atangana–Baleanu operator are used to create a hybrid fractional order model that helps analyze the dynamic transmission of the measles virus. We assess the measles-free and endemic equilibrium, reproductive number, biological viability, boundedness, well-posedness, and positivity of the model. We apply the Banach contraction principle to verify the uniqueness of the system's solutions. The proposed system is confirmed to be Ulam–Hyres stable by using fixed point theory results. The aforementioned operators are further analyzed, and the Laplace-Adomian decomposition method is used to numerically simulate the system of fractional differential equations. To support our findings, the outcomes are graphically displayed. The efficacy and memory impact of fractional operators are illustrated through comparisons. Based on fractional parameter values, the study determines important disease-control strategies and shows that vaccinations greatly reduce the spread of measles. By reducing the number of infected people, increasing vaccination coverage lowers the burden of disease on the general population. • Measles persists as one of the top causes of fatalities among younger kids globally. • For investigation of the dynamical transmission of measles with CP Caputo and ABC. • We checked out the positivity, boundedness, well-posedness, biological viability, and stablity of model. • Numerically simulated a framework of fractional differential equations with the use of the Laplace-Adomian Decomposition method. • A comparison of the proposed scheme is also discussed to show the efficiency and memory effect of the fractional operator. [ABSTRACT FROM AUTHOR]

In this paper, studying a sustainable approach to see the dynamics of infection in the plant by using a fractal fractional derivative. To depict a time-fractional order plant virus model including disease consequences, we suggested a set of fractional differential equations. For the fractional order system, both qualitative and quantitative studies are carried out. To prove the existence and uniqueness of the proposed model with the effect of global derivative, Linear growth and Lipschitz conditions are used. Positiveness and boundedness of solutions of the fractional order model are verified. Local stability analysis and global stability is verified by using the Lyapunov function with the first and second derivative tests. Sensitivity analysis is performed to see the influence of parameters on the fractional order model. To study the effect of the fractional operator, which demonstrates the impact of the illness on plants, solutions are generated with a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel. To observe the behavior of the fractional order plant virus model, numerical simulation is used. Such an inquiry will help to comprehend how the virus behaves and to create defences against infected plants. • Studying a sustainable approach for the dynamics of infection in the plant with fractional derivative. • Analysis of equilibrium points gives the uniqueness and existence of the model. • Both sensitivity and qualitative analysis examined of the fractional order system are performed. • Analysis of the Lyapunov function for global stability is verified, Also, linear growth and Lipschitz condition. • Solutions are generated with a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel. [ABSTRACT FROM AUTHOR]