Determination of the order of fractional derivative for subdiffusion equation

TL;DR

This paper addresses the inverse problem of uniquely determining the fractional derivative order in a subdiffusion equation using fixed-time observation data, crucial for accurate fractional modeling in applied sciences.

Contribution

It proves the unique identifiability of the fractional derivative order from limited observation data in a subdiffusion equation with a general elliptic operator.

Findings

The order of the fractional derivative can be uniquely identified from a single time snapshot.

The method applies to equations with arbitrary second order elliptic operators.

The result enhances the understanding of parameter identification in fractional differential equations.

Abstract

The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as "the observation data", identifies uniquely the order of the fractional derivative.