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Controllability Results of Hilfer Fractional Derivative Through Integral Contractors

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Abstract

The paper sheds light on Hilfer’s controllability facts of neutral fractional system. Originally, the mild solution is derived using semigroup theory and the Laplace transform approach. Controllability of the Hilfer fractional system in non-dense domain using integral contractor which employs the sequence technique with the advantage that the nonlinear function does not meet the Lipschitz condition. To support the computed results, an appropriate examples are discussed.

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Acknowledgements

This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamilnadu, India

    K. Jothimani

  2. Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, 641 202, Tamilnadu, India

    N. Valliammal

  3. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia

    S. Alsaeed & Kottakkaran S. Nisar

  4. Applied Sciences College, Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 715, 21955, Makkah, Saudi Arabia

    S. Alsaeed

  5. Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, 641 029, Tamilnadu, India

    C. Ravichandran

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  1. K. Jothimani
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  2. N. Valliammal
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  3. S. Alsaeed
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  4. Kottakkaran S. Nisar
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  5. C. Ravichandran
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Contributions

onceptualization, KJ, NV; Formal analysis, SA, KSN; Investigation, KJ, NV, CR; Software, SA, CR, KSN; Validation, KSN, CR; Writing – original draft, KJ, NV, KSN, CR; Revision, Review and editing, SA, KSN, CR.

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Correspondence to S. Alsaeed or Kottakkaran S. Nisar.

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Jothimani, K., Valliammal, N., Alsaeed, S. et al. Controllability Results of Hilfer Fractional Derivative Through Integral Contractors. Qual. Theory Dyn. Syst. 22, 137 (2023). https://doi.org/10.1007/s12346-023-00833-9

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  • DOI: https://doi.org/10.1007/s12346-023-00833-9

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