OICC Press Mathematical Sciences 2251-7456 19 4 (December 2025) 2025 12 31 Approximate solution for the fractional Riccati/Logistic differential equations employing the β-Khalouta decomposition technique 10.57647/mathsci.2025.1904.19 EN Mohamed Meabed Khader Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA https://orcid.org/0000-0003-3844-139X Khaled Lotfy Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt Asim Alawfi Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA https://orcid.org/0009-0000-8398-9413 Mohamed Adel Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA https://orcid.org/0000-0001-7069-697X Journal Article 2025 12 31 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.