A generalized Legendre–Gauss collocation method for solving nonlinear fractional differential equations with time varying delays

Abstract

We introduce a new numerical plan for nonlinear autonomous fractional differential equations with time varying delay. Generalized Legendre polynomials and their properties are developed for deriving a general procedure for solving a class of fractional differential equations. The application of the Laplace transform and generalized Legendre polynomials for solving the fractional differential equations with time varying delays is explained. Also, the properties and convergence of the proposed method are surveyed by some theorems. Finally, some numerical examples are implemented to show the efficiency and accuracy of the proposed method. The numerical result shows that the suggested method has high accuracy compared with the existing methods.