This inquire about ponder is committed to investigating a few properties in connection to behaviors of solutions to an extended fractional structure of the standard jerk equation. Here, we define the scheme of the general fractional jerk problem using the generalized $G$ operators. The existence result of such a new model is derived and analyzed based on some inequalities and fixed point tools. Furthermore, analysis of its Ulam-Hyers-Rassias type stability is performed and finally, we give numerical simulations for the existing parameters of the mentioned fractional $G$-jerk system in the Katugampola, Caputo-Hadamard and Caputo settings under different arbitrary orders.
