Chaotic systems play a crucial role in science and engineering due to their complex and unpredictable behavior. In this study, we investigated a nonlinear chaotic system known as the multi-bond orbital chaotic attractor (MBOCA), which we modeled using the Caputo Fabrizio fractional operators. We first established the existence and uniqueness of solutions for the system after applying these operators to the MBOCA. We then presented a numerical scheme and analyzed its stability and convergence. To validate the proposed numerical scheme, we performed numerical simulations to visualize the system's behavior for both integer and fractional order cases. The results confirmed that the generated bond-orbital attractors exhibit chaotic behavior, highlighting the influence of fractional order operators on the system's dynamic complexity.