Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions

•Multi-scale orthogonal basis method is used for the considered equation.•The error estimation and stable analysis are presented in detailed. In this paper, we investigate the multi-scale orthogonal basis method for fractional integral boundary value problems. We apply the Newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi-scale orthogonal basis, then the approximation solution is obtained. The error estimation and stable analysis are presented in detailed. The final numerical experiments verify that the accuracy of our method.