An effective operational matrix method based on shifted sixth-kind Chebyshev polynomials for solving fractional integro-differential equations with a weakly singular kernel

The principal aim of this study is to present a new algorithm for solving some kinds of weakly singular fractional integro-differential equations. The suggested algorithm uses the shifted sixth -kind Chebyshev polynomials together with the collocation method. Using the suggested algorithm and resultant operational matrices, the main equation converts into a system of algebraic equations which can be efficiently solved. Some theorems are proved and used to deduce an upper error bound for this method. Also, several examples are presented to illustrate the efficiency of the suggested algorithm compared to other methods in the literature. The suggested algorithm provides accurate results, even using a few terms of the proposed expansion.