Fractional Order Runge–Kutta Methods

This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution differential equations (FDEs). We construct explicit and implicit FORK FDEs by using Caputo generalized Taylor series formula. Due to dependence derivatives on fixed base point, in proposed method, we had modify right-hand side given equation all steps methods. Some coefficients schemes are presented. The convergence analysis method is also discussed. Numerical experiments presented clarify effectiveness robustness method.