Time fractional exact controllability
Paola Loreti, Daniela Sforza
TL;DR
This paper extends the Hilbert Uniqueness Method to fractional diffusion-wave equations, addressing the challenge of defining an appropriate adjoint system for exact controllability.
Contribution
It introduces a novel adaptation of HUM for fractional PDEs, specifically fractional diffusion-wave equations, which was not previously established.
Findings
Successfully formulated the adjoint system for fractional equations
Demonstrated the applicability of HUM to fractional PDEs
Provided a framework for future controllability studies in fractional systems
Abstract
Our purpose is to adapt the Hilbert Uniqueness Method by J.-L. Lions in the case of fractional diffusion-wave equations. The main difficulty is to determine the right shape for the adjoint system, suitable for the procedure of HUM.
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Taxonomy
TopicsFractional Differential Equations Solutions · Numerical methods for differential equations · Stability and Controllability of Differential Equations