The current investigations are related to indicate a competent numerical fractional Meyer neural network (FMNN) procedure using the optimization of genetic algorithm and interior-point algorithm (GAIPA), i.e., FMNN-GAIPA for solving the Bagley–Torvik model (BTM). A merit function based on the differential BTM form, and its corresponding initial conditions is constructed and then optimized with the FMNN-GAIPA. Three different BTM cases will be solved through the FMNN-GAIPA and the correctness of the proposed FMNN-GAIPA is observed by using the comparison for each case of the BTM with the exact solutions. The statistical investigations based on the appropriate large independent trials recognized the constancy of the FMNN-GAIPA in terms of robustness, convergence, and stability trials. In addition, the annotations over the statistical measures validate the values of FMNN-GAIPA.