In this study, we employed a novel technique with the help of the iterative method (DGJM) to solve the generalized time-fractional Cattaneo model (GTFCM). The existence and uniqueness of the solutions for this fractional model are examined using Banach’s fixed-point theorem. Additionally, the stability of the solutions is evaluated under Ulam-Hyers conditions. The fractional order derivative is calculated by using the Caputo derivative with order   1 < α < 2 . We compared our results with the exact solution and other existing techniques, demonstrating that our approach is efficient.