Analysis of Huanglongbing disease model with a novel fractional piecewise approach

Huanglongbing (yellow dragon disease), often known as citrus greening, is one of the world's most destructive citrus illnesses. It is caused by Candidatus Liberibacter asiaticus, a bacterial disease that spreads through the tree canopy, causing the tree to degrade and eventually die. The aim of this paper is to study the dynamics of the Huanglongbing disease model using the novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, while the non-singular kernel is the Atangana-Baleanu Caputo operator. The existence and uniqueness of the solution with piecewise derivatives are examined for the aforementioned problem. The suggested problem's approximate solution is obtained using the piecewise numerical iterative scheme based on the Newton polynomial approach. The numerical simulation for the piecewise derivable problem under consideration is presented using the data for various fractional orders. From the simulations, it is observed that when the vaccination rate is high then the number of exposed and infected citrus trees is small as compared to the lower vaccination rates.