Regional enlarged observability of Caputo fractional differential equations

TL;DR

This paper addresses the regional enlarged observability problem for fractional evolution differential equations with Caputo derivatives, demonstrating the possibility of reconstructing initial states within a subregion using the Hilbert Uniqueness Method.

Contribution

It introduces a novel approach to regional observability for fractional differential equations involving Caputo derivatives, utilizing the Hilbert Uniqueness Method.

Findings

Reconstruction of initial states in a subregion is feasible.

The Hilbert Uniqueness Method is effective for fractional differential equations.

An illustrative example validates the theoretical results.

Abstract

We consider the regional enlarged observability problem for fractional evolution differential equations involving Caputo derivatives. Using the Hilbert Uniqueness Method, we show that it is possible to rebuild the initial state between two prescribed functions only in an internal subregion of the whole domain. Finally, an example is provided to illustrate the theory.