Complex dynamics of multi strain TB model under nonlocal and nonsingular fractal fractional operator

Abstract

Researchers have recently begun to use fractal fractional operators in the Atangana–Baleanu sense to analyze complicated dynamics of various models in applied sciences, as the Atangana–Baleanu operator generalizes the integer and fractional order operators. To analyze the complex dynamics of the multi-strain TB model, we use the AB-fractal fractional operator. We use the Banach fixed point theorem to ensure that at most one solution exists to the model. Further, the Ulam–Hyers type stability of the model is investigated with the help of functional analysis. The Adams–Bashforth approach is used to get numerical results for the proposed model. The analysis of the chaotic behavior of the proposed TB model was missing in the literature. Therefore, for different values of fractional and fractal order, we study the nonlinear dynamics and chaotic behavior of the obtained results of the proposed model.