Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives
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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.
Axioms 2018, 7(4), 92; https://doi.org/10.3390/axioms7040092
Received: 4 November 2018
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Revised: 25 November 2018
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Accepted: 28 November 2018
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Published: 1 December 2018
(This article belongs to the Special Issue Fractional Differential Equations)
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.
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Keywords:
fractional evolution systems; Riemann–Liouville time derivatives; enlarged observability; regional reconstruction; HUM approach
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MDPI and ACS Style
Zouiten, H.; Boutoulout, A.; Torres, D.F.M. Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives. Axioms 2018, 7, 92. https://doi.org/10.3390/axioms7040092
AMA Style
Zouiten H, Boutoulout A, Torres DFM. Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives. Axioms. 2018; 7(4):92. https://doi.org/10.3390/axioms7040092
Chicago/Turabian StyleZouiten, Hayat, Ali Boutoulout, and Delfim F.M. Torres. 2018. "Regional Enlarged Observability of Fractional Differential Equations with Riemann—Liouville Time Derivatives" Axioms 7, no. 4: 92. https://doi.org/10.3390/axioms7040092
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