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On the controllability of fractional semilinear systems via the generalized Hattaf fractional derivative

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Abstract

The purpose of this paper is to investigate the controllability of a semilinear system including the generalized Hattaf fractional \(\mathcal {GHF}\) derivative. First, the Laplace transform is used to solve the \(\mathcal {GHF}\) system. To study the controllability of linear \(\mathcal {GHF}\) systems, we compute the fractional controllability Gramian matrix and we derive the sufficient conditions. Based on the controllability of the linear system and the Schauder fixed-point theorem, sufficient conditions for controllability are established using the fixed-point theory for semilinear \(\mathcal {GHF}\) systems. Finally, an example is given to confirm our theoretical findings.

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Authors and Affiliations

  1. Superior School of Technology, LASTIMI, Mohammed V University, Sale, Morocco

    Mohamed Reda Lemnaouar & Younes Louartassi

  2. Faculty of Sciences, Lab-Mia, Mohammed V University, Rabat, Morocco

    Chaimaa Taftaf & Younes Louartassi

Authors
  1. Mohamed Reda Lemnaouar
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  2. Chaimaa Taftaf
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  3. Younes Louartassi
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All the authors have contributed equally to this paper.

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Correspondence to Mohamed Reda Lemnaouar.

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Thank you for giving us the opportunity to submit a revised draft of our manuscript entitled “On the controllability of fractional semilinear systems via the generalized Hattaf fractional derivative” to the International Journal of Dynamics and Control. We appreciate the time and effort that you and the reviewers have dedicated to providing your valuable feedback on our manuscript. We are grateful to the reviewers for their insightful comments on our paper

All authors have contributed equally to this document.

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Lemnaouar, M.R., Taftaf, C. & Louartassi, Y. On the controllability of fractional semilinear systems via the generalized Hattaf fractional derivative. Int. J. Dynam. Control 12, 2050–2057 (2024). https://doi.org/10.1007/s40435-023-01320-4

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  • DOI: https://doi.org/10.1007/s40435-023-01320-4

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