Numerical solution of two and three-dimensional fractional heat conduction equations via Bernstein polynomials

In this paper, we develop a new scheme for the numerical solution of the two- and three-dimensional fractional heat conduction equations on a rectangular plane. Our main aim is to characterize the Bernstein operational matrices of derivative and integration in the two and three-dimensional cases and then apply them for solving the mentioned problems. This work causes to reduce the solution of fractional differential equations to the solution of an algebraic equation system. The presented method is applied to solve several problems. Approximated solutions are compared with the exact solutions which results show a negligible error.