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Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Author

Listed:
  • Lakshman Mahto

    (Department of Science and Humanities, Indian Institute of Information Technology Dharwad, Hubli 580029, India)

  • Syed Abbas

    (School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., India)

  • Mokhtar Hafayed

    (Laboratory of Applied Mathematics, Biskra University, Biskra 07000, Algeria)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

Abstract

In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ∈ ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain.

Suggested Citation

  • Lakshman Mahto & Syed Abbas & Mokhtar Hafayed & Hari M. Srivastava, 2019. "Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition," Mathematics, MDPI, vol. 7(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:190-:d:206669
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    References listed on IDEAS

    as
    1. Meili Li & Haiqiang Liu, 2010. "An Existence Result for Second-Order Impulsive Differential Equations with Nonlocal Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-9, August.
    2. Mahmudov, N.I., 2018. "Partial-approximate controllability of nonlocal fractional evolution equations via approximating method," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 227-238.
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