| Summary: | This scientific study investigates to check the dynamical behavior of yellow virus in red chilli with fractional order techniques. While attempts are being made to stop the yellow virus pandemic, a more infectious yellow virus found in red chilli is developing in many locations. It is crucial to learn how to create strategies that will stop the yellow virus’s spread to mimic the propagation of the yellow virus in red chilli plants while maintaining a specific degree of immunity. As a case study, we looked at the possibility of an outbreak in red chilli plants. Recently, novel fractal-fractional operators proposed by Atangana have been widely used to observe the unanticipated elements of a problem. Currently, the illness caused by the yellow virus in red chilli is common and difficult to treat. The inventive operators have been implemented in this structure to observe the influence of vaccination on the yellow virus in the red chilli model using a variety of values for υ1 and υ2 which are utilized to represent the impact of vaccination. The number of reproductions will determine whether the system is clear of sickness. Using the fractal-fraction Mittag–Leffler operator, we examined the qualitative and quantitative characteristics of the yellow virus in the red chilli model. The results of the fixed point theory are used to apply an improved method for the fractional order model of the yellow virus. Nonlinear analysis was used to assess the stability of the Ulam-Hyres. Numerical simulations are demonstrated to prove the efficiency of the proposed method. The tools employed in this model appear to be quite potent and capable of simulating the expected theoretical conditions in the issue.
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