Abstract
The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana-Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem's approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer.