# American Institute of Mathematical Sciences

March  2020, 13(3): 1017-1029. doi: 10.3934/dcdss.2020060

## 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

Received  April 2018 Revised  July 2018 Published  March 2019

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

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.

Citation: Hayat Zouiten, Ali Boutoulout, Delfim F. M. Torres. Regional enlarged observability of Caputo fractional differential equations. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 1017-1029. doi: 10.3934/dcdss.2020060
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