Investigation of mathematical model of transmission co-infection TB in HIV community with a non-singular kernel

The current manuscript deals with the fractional dynamical system of transmission along with co-infection of TB in the HIV community including ten classes. We study the necessary conditions for the existence and uniqueness of the solution of the considered system under the fractional operator known as Atangana–Baleanu in Caputo sense. By using fixed-point theory, the qualitative analysis of the result and Ulam–Hyers stability involving fractional operator for the proposed system is derived. For numerical simulations, we applied the fractional Adams–Bashforth method to the system. The obtained results are demonstrated explicitly to illustrate the validity of the considered technique for solving the proposed model under the above-mentioned operator. We observed that, if HIV-infected or unprotected individuals are in contact with TB infected individuals, the disease will grow in society. The dynamical behavior is shown for different arbitrary orders between 0 and 1, which converges to the integer-order one.