A reproducing kernel method for nonlinear C-q-fractional IVPs

Here a scheme for solving the Caputo type q-fractional (C-q-fractional) initial value problems (IVPs) in reproducing kernel spaces is given. By the attribute of the q-fractional operator, we first convert the q-fractional differential problems into q-fractional Volterra integral problems. Then, we implement the Quasi-Newton’s method (QNM) to linearize the nonlinear equations. Finally, based on the theory of reproducing kernel method (RKM), a stable numerical scheme is proposed to resolve the linear equations. The reliability and efficiency are verified by numerical experiments.