Akkilic, Ayse NurUmar, MuhammadSalahshour, SoheilBulut, Hasan2025-11-152025-11-1520252190-544410.1140/epjp/s13360-025-06940-72-s2.0-105019507542https://doi.org/10.1140/epjp/s13360-025-06940-7https://hdl.handle.net/20.500.14517/8516Motivation: The present research is investigating the numerical performances of the fractional-order nonlinear model of the human immunodeficiency virus (HIV) infection system of T-cells or CD4+ T-cells by implementing a computational stochastic scheme. The mathematical fractional-order HIV model is presented in concentration of susceptible cells, septic T-cells-based HIV, and free HIV virus elements in the blood. Method: The structure of the solver is designed by the Levenberg-Marquardt backpropagation neural network (LMBNN), activation radial basis (RB) function in the single hidden layer with fifteen number of neurons. A reference data are obtained through the improved Euler method, which is tested through the proposed solver by taking the statistics 80% for training, 10% for testing, and 10% for authentication. Results: The approximate outcomes obtained through the designed solver are compared with the reference outcomes, which perform the correctness of the scheme. Moreover, the negligible absolute error measures together with different tests including state transition, error histogram, and correlation validate the correctness of the proposed procedure. Novelty: The designed neural network process using the LMBNN together with the RB activation function has never been implemented before to present the results of the fractional-order HIV model.eninfo:eu-repo/semantics/closedAccessArticle