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.

目前的手稿涉及 HIV 社区中传播的分数动力系统以及 TB 的合并感染，包括 10 个类别。我们研究了在 Caputo 意义上称为 Atangana-Baleanu 的分数算子下所考虑系统的解的存在性和唯一性的必要条件。通过使用不动点理论，对所提出的系统的结果和涉及分数算子的 Ulam-Hyers 稳定性进行了定性分析。对于数值模拟，我们将分数 Adams-Bashforth 方法应用于系统。所获得的结果被明确地证明，以说明所考虑的技术在上述算子下求解所提出的模型的有效性。我们观察到，如果艾滋病毒感染者或未采取保护措施的人与结核病感染者接触，这种疾病就会在社会中蔓延。显示了 0 到 1 之间不同任意阶数的动力学行为，收敛到整数阶一。