spectral method for third-kind volterra integral equation

This present work will focus on the spectral approach to a class of third-kind volterra integral equation using the boubaker polynomials as a basis function. in this approach, the operational matrix of fractional integration and the operational matrix of multiplication are utilized. the strategy that adopts here is expanding the unknown function in terms of boubaker polynomials with unknown coefficients. then, by using the given operational matrices, the problem under study is reduced to a problem easier to solve. the error bound of the suggested approximation is investigated. some examples are implemented to display the efficiency and applicability of the recommended scheme.