We provide an approximation solution to the Riccati/Logistic differential equations (RDE/LDE) with the CaputoKatugampola fractional derivative. The proposed methodology relies on the 𝛽-Khalouta decompositionmethod (𝛽-KDM). The proposed approach integrates the 𝛽-Khalouta transform method with a decomposition technique. The stability study encompasses the uniqueness, convergence, and error estimation of the proposed scheme. The residual error function is computed and utilized as a fundamental criterion for assessing the accuracy and efficiency of the specified numerical method. We employ the exact solution and the fourth-order Runge-Kutta method for comparison with the results obtained from the employed method. The results confirm that the used method is a straightforward and efficient instrument for the numerical simulation of these models. Illustrative models are provided to validate the efficacy and utility of the suggested approach.