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 estimate all three parameters simultaneously. Numerical results are presented with noisy measurements to show the effectiveness and the robustness of the proposed method. 
Abeer Aldoghaither and Taous-Meriem Laleg-Kirati and Da-Yan Liu
math.OC