(untitled) (Contemporary Mathematics, 2025)
Fractional calculus concept has proven to be a great, powerful, and effective tool in analyzing mathematical models across diverse various fields of scientific and engineering domains. A significant feature of this article is to investigate the novel Human T-cell Lymphotropic Virus (HTLV)/Human Papillomavirus (HPV)/Human Immunodeficiency Virus (HIV) multi-infection model, along with a computational numerical study and stability analysis to describe the modified Atangana-Baleanu-Caputo fractional order framework. The model performed stability analysis based on the Ulam-Hyers stability concept can be established by using the solution of existence and uniqueness conditions derived from the fixed-point techniques for the recommended problem. The multi-infection dynamical system behavior is expressed on the approximate solution of a two-step Lagrange interpolation polynomials numerical scheme utilizing a modified Atangana-Baleanu-Caputo fractional order framework, with all implementation and simulations conducted in Matrix Laboratory (MATLAB). Overall judgment shows that the numerical results of the recommended method significantly impact the multi-infection model behavior.