A Novel Approach for Parameter and Differentiation Order Estimation for a Space Fractional Advection Dispersion Equation

In this paper, we propose a new approach, based on the so-called modulating functions to estimate the average velocity, the dispersion coefficient and the differentiation order in a space fractional advection dispersion equation. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with Newton’s method is applied to esti-mate all three parameters simultaneously. Numerical results are presented with noisy measurements to show the effectiveness and the robustness of the proposed method. keywords space fractional advection dispersion equation; modulating functions; parameter estimation