 This work presents a design for a Newton-Liednik system with a fractional Caputo-Fabrizio derivative to explain its chaotic characteristics. The time-varying fractional Caputo-Fabrizio derivative approach is applied to solve the model numerically and to check the solution's existence and uniqueness. The existence and uniqueness of results of a fractional order model under the Caputo-Fabrizio fractional operator have been proved by fixed-point theory. Chaos is controlled by linear controllers, and the Lyapunov exponent of the system indicates that the chaos control findings are accurate. Based on weighted covariant Lyapunov vectors, we construct a background covariance matrix using the Kaplan-York dimension. Using a numerical example, this suggested method is illustrated for its applicability and efficiency. This article was authored by Najat Al-Mutairi and Sate Saber.