In this paper, we introduce a numerical treatment using the generalized Euler method (GEM) for the fractional (Caputo sense) Riccati and Logistic differential equations. In the proposed method, we invert the given model as a difference equation. We compare our numerical solutions with the exact solution and with those numerical solutions using the fourth-order Runge-Kutta method (RK4). The obtained numerical results of the two proposed problem models show the simplicity and efficiency of the proposed method.
Khader, M. M.; Sweilam, N. H.; and Kharrat, B. N.
Numerical Simulation for Solving Fractional Riccati and Logistic Differential Equations as a Difference Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 37.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/37