Bernstein polynomials based iterative method for solving fractional integral equations

Abstract A novel iterative numerical method is constructed for solving second kind Volterra fractional integral equations. The method uses at each iterative step a Bernstein spline interpolation procedure combined with the corresponding quadrature formula. In this way, based on the nice approximation and shape preserving properties of the Bernstein polynomials, we propose an alternative to the classical product integration technique that uses trapezoidal, Simpson, Gauss type and other well-known quadrature formulas. The convergence of the method is proved with the error estimate expressed in terms of the Lipschitz constants and the accuracy is illustrated on some numerical experiments.