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Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems

Author

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  • Asmae Tajani

    (Moulay Ismail University, Faculty of Sciences)

  • Fatima-Zahrae El Alaoui

    (Moulay Ismail University, Faculty of Sciences)

Abstract

The main objective of this work is to steer a semilinear time-fractional diffusion control system involving Riemann–Liouville fractional derivative to a desired state in a part of the boundary of the evolution domain. For that, we use fixed point technique, semigroup theory and fractional calculus under some proposed assumptions in the linear part of the system and the nonlinear term. At the end, we provide some numerical simulations which lead to successful figures, in order to guarantee the efficiency of the proposed approach.

Suggested Citation

  • Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02248-7
    DOI: 10.1007/s10957-023-02248-7
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    References listed on IDEAS

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    1. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    2. Ricardo Enrique Gutiérrez & João Maurício Rosário & José Tenreiro Machado, 2010. "Fractional Order Calculus: Basic Concepts and Engineering Applications," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, May.
    3. Kavitha, K. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy & Udhayakumar, R., 2021. "Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Asmae Tajani & Fatima Zahrae El Alaoui & Ali Boutoulout, 2020. "Regional Controllability of Riemann–Liouville Time-Fractional Semilinear Evolution Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, November.
    5. Tajani, Asmae & El Alaoui, Fatima-Zahrae & Boutoulout, Ali, 2022. "Regional boundary controllability of semilinear subdiffusion Caputo fractional systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 481-496.
    6. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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