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

TL;DR

This paper introduces a new modulating functions-based method to accurately estimate parameters and the differentiation order in space fractional advection dispersion equations, demonstrating robustness with noisy data.

Contribution

It presents a novel combined approach using modulating functions and Newton's method for simultaneous parameter and order estimation in fractional PDEs.

Findings

Effective parameter estimation with noisy data

Robustness demonstrated through numerical simulations

Simultaneous estimation of multiple parameters

Abstract

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.