Analysis of dual Bernstein operators in the solution of the fractional convection–diffusion equation arising in underground water pollution

The Bernstein operators (BO) are not orthogonal, but they have duals, which are obtained by a linear combination of BO. In recent years dual BO have been adopted in computer graphics, computer aided geometric design, and numerical analysis. This paper presents a numerical method based on the Bernstein operational matrices to solve the time–space fractional convection–diffusion equation. A generalization of the derivative matrix operator of fractional order and the error analysis are discussed. Numerical examples compare the proposed approach with previous works, showing that the method is more accurate and efficient.