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Exact Controllability of Multi-Term Time-Fractional Differential System with Sequencing Techniques

Author

Listed:
  • Vikram Singh

    (Indian Institute of Technology Roorkee)

  • Dwijendra N. Pandey

    (Indian Institute of Technology Roorkee)

Abstract

In this paper, an abstract multi-term time-fractional differential system is considered and the existence, uniqueness and exact controllability results are investigated. In this theory, we use the notion of bounded integral contractor introduced by Altman to come up with a new set of sufficient conditions for the exact controllability by constructing a sequencing technique. Moreover, in this technique, we are not required to define induced inverse operator and Lipschitz continuity of nonlinear functions. Finally, an application is given to illustrate the obtained results.

Suggested Citation

  • Vikram Singh & Dwijendra N. Pandey, 2020. "Exact Controllability of Multi-Term Time-Fractional Differential System with Sequencing Techniques," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 105-120, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0387-7
    DOI: 10.1007/s13226-020-0387-7
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    References listed on IDEAS

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    1. Giona, Massimiliano & Cerbelli, Stefano & Roman, H.Eduardo, 1992. "Fractional diffusion equation and relaxation in complex viscoelastic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 449-453.
    2. Lizzy, R. Mabel & Balachandran, Krishnan & Trujillo, Juan J., 2017. "Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 162-167.
    3. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
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