Regional enlarged observability of Caputo fractional differential equations

Hayat Zouiten; Ali Boutoulout; Delfim F. M. Torres

doi:10.3934/dcdss.2020060

Article Contents

2020, Volume 13, Issue 3: 1017-1029. Doi: 10.3934/dcdss.2020060

This issue Previous Article MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination Next Article

Regional enlarged observability of Caputo fractional differential equations

1.
TSI Team, MACS Laboratory, Department of Mathematics and Computer Science, Moulay Ismail University, Faculty of Sciences, 11201 Meknes, Morocco
2.
Center for Research & Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810–193 Aveiro, Portugal

^* Corresponding author: delfim@ua.pt
^* Corresponding author: delfim@ua.pt

Received: March 31, 2018

Revised: June 30, 2018

Published: December 2019

This research is part of first author's Ph.D. project, which is carried out at Moulay Ismail University, Meknes

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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.

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Mathematics Subject Classification: Primary: 35R11, 93B07; Secondary: 26A33, 93C20.

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