Ordinary differential equations describe several phenomena in different fields of engineering and physics. Our aim is to use the reproducing kernel Hilbert space method (RKHSM) to find a solution to some ordinary differential equations (ODEs) that are described by using the global derivative. In this research, we used the RKHSM to construct new numerical solutions for nonlinear ODEs with global derivative. The used method systematically produces analytic and approximate solutions in the series’s form. We tested three applications for showing the performance of the RKHSM.