The convergence and stability analysis of the Jacobi collocation method for solving nonlinear fractional differential equations with integral boundary conditions

Abstract

In this paper, we apply the Jacobi collocation method for solving nonlinear fractional differential equations with integral boundary conditions. Due to existence of integral boundary conditions, after reformulation of this equation in the integral form, the method is proposed for solving the obtained integral equation. Also, the convergence and stability analysis of the proposed method are studied in two main theorems. Furthermore, the optimum degree of convergence in the L 2 norm is obtained for this method. Furthermore, some numerical examples are presented in order to illustrate the performance of the presented method. Finally, an application of the model in control theory is introduced.