Unique identification of fractional orders in the fractional mobile–immobile solute transport system

Abstract

This article deals with a fractional mobile–immobile solute transport system in porous media and an inverse problem of identifying the fractional orders by the additional measurements at one interior point. The unique existence of a solution to the forward problem is obtained based on the inverse Laplace transform, and the uniqueness of the inverse problem is proved in the real space of Laplace transform by the maximum principle. Numerical inversions with noisy data are presented to support the uniqueness result of the inverse problem.

Keywords

• fractional solute transport system
• laplace transform
• inverse problem
• uniqueness
• numerical inversion