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Axioms 2018, 7(4), 92; https://doi.org/10.3390/axioms7040092

Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives

1
TSI Team, MACS Laboratory, Department of Mathematics and Computer Science, Moulay Ismail University, Faculty of Sciences, Meknes 11201, Morocco
2
Center for Research & Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
*
Author to whom correspondence should be addressed.
Received: 4 November 2018 / Revised: 25 November 2018 / Accepted: 28 November 2018 / Published: 1 December 2018
(This article belongs to the Special Issue Fractional Differential Equations)
Full-Text   |   PDF [307 KB, uploaded 17 December 2018]

Abstract

We introduce the concept of regional enlarged observability for fractional evolution differential equations involving Riemann–Liouville derivatives. The Hilbert Uniqueness Method (HUM) is used to reconstruct the initial state between two prescribed functions, in an interested subregion of the whole domain, without the knowledge of the state. View Full-Text
Keywords: fractional evolution systems; Riemann–Liouville time derivatives; enlarged observability; regional reconstruction; HUM approach fractional evolution systems; Riemann–Liouville time derivatives; enlarged observability; regional reconstruction; HUM approach
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zouiten, H.; Boutoulout, A.; Torres, D.F.M. Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives. Axioms 2018, 7, 92.

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