A new stable collocation method for solving a class of nonlinear fractional delay differential equations

In this paper, a stable collocation method for solving the nonlinear fractional delay differential equations is proposed by constructing a new set of multiscale orthonormal bases of W-2,0(1). Error estimations of approximate solutions are given and the highest convergence order can reach four in the sense of the norm of W-2,0(1). To overcome the nonlinear condition, we make use of Newton's method to transform the nonlinear equation into a sequence of linear equations. For the linear equations, a rigorous theory is given for obtaining their epsilon-approximate solutions by solving a system of equations or searching the minimum value. Stability analysis is also obtained. Some examples are discussed to illustrate the efficiency of the proposed method.