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An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain

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  • Nisar, Kottakkaran Sooppy
  • Jothimani, K.
  • Kaliraj, K.
  • Ravichandran, C.

Abstract

In this article, the controllability results of the non-dense Hilfer neutral fractional derivative (HNFD) are presented. The results are acknowledged using semigroup theory, fractional calculus, Banach contraction principle, and Mönch technique. Moreover, a numerical analysis is given to enhance our model.

Suggested Citation

  • Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002691
    DOI: 10.1016/j.chaos.2021.110915
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    References listed on IDEAS

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    1. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Xue Pan & Xiuwen Li & Jing Zhao, 2014. "Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    3. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    4. Jun Du & Wei Jiang & Denghao Pang & Azmat Ullah Khan Niazi, 2018. "Exact Controllability for Hilfer Fractional Differential Inclusions Involving Nonlocal Initial Conditions," Complexity, Hindawi, vol. 2018, pages 1-13, August.
    5. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
    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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    Cited by:

    1. Veeresha, P., 2022. "The efficient fractional order based approach to analyze chemical reaction associated with pattern formation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Lakshmi Priya, P.K. & Kaliraj, K., 2022. "An application of fixed point technique of Rothe’s-type to interpret the controllability criteria of neutral nonlinear fractional ordered impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Kaliraj, K. & Manjula, M. & Ravichandran, C., 2022. "New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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