Parameter and differentiation order estimation for a two dimensional fractional partial differential equation

This paper deals with the estimation of coefficients and differentiation orders for two-dimensional fractional partial differential equations. Recently, a hybrid method based on modulating functions has been proposed by the authors to estimate the coefficients and a differentiation order for a one dimensional fractional advection dispersion equation in Aldoghaither et al. (2015). We propose to extend this method to the two-dimensional case. First, the coefficients are estimated using a modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with a Newton algorithm is proposed to estimate the coefficients and the differentiation orders simultaneously. Numerical example is presented with noisy measurements to show the effectiveness and the robustness of the method.