On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients

TL;DR

This paper investigates inverse problems for uncoupled space-time fractional operators with time-dependent coefficients, establishing unique determination results using advanced fractional calculus techniques.

Contribution

It extends unique determination results from space-fractional to space-time fractional operators by developing new analytical tools and approximation properties.

Findings

Derived the Runge approximation property for space-time fractional operators

Extended unique determination results to space-time fractional case

Utilized integration by parts for Riemann-Liouville and Caputo derivatives

Abstract

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the Dirichlet-to-Neumann map. We exploit the integration by parts formula for Riemann-Liouville and Caputo derivatives to derive the Runge approximation property for our space-time fractional operator based on the unique continuation property of the fractional Laplacian. This enables us to extend early unique determination results for space-fractional but time-local operators to the space-time fractional case.