A novel algorithm to solve nonlinear fractional quadratic integral equations

This paper addresses a new spectral collocation method for solving nonlinear fractional quadratic integral equations. The main idea of this method is to construct the approximate solution based on fractional order Chelyshkov polynomials (FCHPs). To this end, first, we introduce these polynomials and express some of their properties. The operational matrices of fractional integral and product are derived. The spectral collocation method is utilized together with operational matrices to reduce the problem to a system of algebraic equations. Finally, by solving this system, the unknown coefficients are computed. Further, the convergence analysis and numerical stability of the method are investigated. The proposed method is computationally simple and easy to implement in computer programming. The accuracy and applicability of the method is presented by some numerical examples.