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Stabilization of fractional parabolic equations through designed robust Robin boundary controller

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  • Arfaoui, Hassen

Abstract

The paper deals with the boundary stabilization for time-fractional parabolic equations (TFPEs) with non-constant coefficients and distributed disturbance by backstepping approach. Firstly, boundary stabilization is investigated through right Robin boundary control (RRBC) with homogeneous left Robin boundary condition at the lower end of the spatial domain. In this context, we proved a Mittag-Leffler stability result for the solution of the TFPEs. To achieve this objective, a robust boundary feedback control law has been designed for the stabilization of the TFPEs by backstepping approach. To the best of our knowledge, the stabilization of TFPEs with left homogeneous Robin boundary condition through right Robin-type boundary feedback control law via backstepping method is novel. Some numerical examples are presented at the end of this paper to confirm the theoretical results.

Suggested Citation

  • Arfaoui, Hassen, 2026. "Stabilization of fractional parabolic equations through designed robust Robin boundary controller," Chaos, Solitons & Fractals, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:chsofr:v:207:y:2026:i:c:s096007792600144x
    DOI: 10.1016/j.chaos.2026.118003
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