Least square shifted Chebyshev method for solving nonlinear fractional integro-differential equations

A numerical method based on the least squares method with the aid of shifted Chebyshev polynomial is applied for solving nonlinear fractional integro-differential equations (FIDEs). The properties of shifted Chebyshev polynomial and least squares method are used to reduce the integro-differential equations to a system of algebraic equations which can be solved by any numerical method. Furthermore, the existence and uniqueness of the method will be shown. The results show that this method is of high accuracy, more convenient, and efficient for solving nonlinear FIDEs.