investigating nonlinear fractional systems: reproducing kernel Hilbert space method

The reproducing kernel Hilbert space method (RK-HS method) is used in this research for solving some important nonlinear systems of fractional ordinary differential equations, such as the fractional Susceptible-Infected-Recovered (SIR) model. Nonlinear systems are widely used across various disciplines, including medicine, biology, technology, and numerous other fields. To evaluate the RK-HS method's accuracy and applicability, we compare its numerical solutions with those obtained via Hermite interpolation, the Adomian decomposition method, and the residual power series method. To further support the reliability of the RK-HS method, the convergence analysis is discussed.