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

Li Li

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arXiv · 2208.05012

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

Li Li

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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.

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Li Li. 2022-08-09. On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients. https://arxiv.org/abs/2208.05012

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