A spectral technique for solving two-dimensional fractional integral equations with weakly singular kernel

This paper adapts a new numerical technique for solving two- dimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equa tions. We apply the reported numerical method to solve several nu merical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional frac tional integral equations with weakly singular.