Numerical algorithm for nonlinear fractional equations with nonlocal boundary conditions based on a modified minimum residual method

Abstract In this paper, we will solve a nonlinear time-fractional equation with nonlocal boundary conditions. First, we construct a set of suitable base according to the correlation theory of reproducing kernel space and the nonlocal boundary conditions. Then we introduce F-derivative and Newton iterative to linearize the nonlinear terms of the equation. The appropriate initial iteration value is constructed by boundary conditions. Finally, we use the ɛ-approximate solution theory to solve the system of linear equations and give the corresponding theoretical derivation. In conclusion, several numerical examples illustrate the feasibility and effectiveness of the method.