Approximate solution for the fractional Riccati/Logistic differential equations employing the β-Khalouta decomposition technique

We provide an approximation solution to the Riccati/Logistic differential equations (RDE/LDE) with the Caputo-Katugampola fractional derivative. The proposed methodology relies on the β Khalouta decomposition method (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. MSC 2000: 26A33; 34A08; 65N06; 65N12.