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Improved order in Hilfer fractional differential systems: Solvability and optimal control problem for hemivariational inequalities

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  • Mohan Raja, Marimuthu
  • Vijayakumar, V.
  • Veluvolu, Kalyana Chakravarthy

Abstract

The main objective of this study is to analyze the optimal control results and solvability concerning Hilfer fractional differential hemivariational inequalities within the range of (1<ϱ<2). Initially, we explore the solvability of a mild solutions for the Hilfer fractional hemivariational inequality. Subsequently, we investigate the optimal control strategies for the given problems by employing cost functionals, cosine operators, mild solutions, the fixed point method for multivalued functions, and a generalized Clarke subdifferential approach. To illustrate our findings, we provide a practical example and a filter diagram.

Suggested Citation

  • Mohan Raja, Marimuthu & Vijayakumar, V. & Veluvolu, Kalyana Chakravarthy, 2024. "Improved order in Hilfer fractional differential systems: Solvability and optimal control problem for hemivariational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s096007792401110x
    DOI: 10.1016/j.chaos.2024.115558
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    References listed on IDEAS

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    1. Dineshkumar, Chendrayan & Jeong, Jae Hoon & Joo, Young Hoon, 2024. "Stochastic exponential stabilization and optimal control results for a class of fractional order equations," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    2. Chen, Weihao & Liu, Yansheng & Zhao, Daliang, 2024. "Approximate controllability for a class of stochastic impulsive evolution system with infinite delay involving the fractional substantial derivative," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Hussain, Sadam & Sarwar, Muhammad & Abodayeh, Kamaleldin & Promsakon, Chanon & Sitthiwirattham, Thanin, 2024. "Controllability of Hilfer fractional neutral impulsive stochastic delayed differential equations with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    4. Jia Wei He & Yong Liang & Bashir Ahmad & Yong Zhou, 2019. "Nonlocal Fractional Evolution Inclusions of Order ? ? (1,2)," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    5. Zhang, Chuanlin & Ye, Guoju & Liu, Wei & Liu, Xuelong, 2024. "On controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    6. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. Jin-Mun Jeong & Sang-Jin Son, 2015. "Time Optimal Control of Semilinear Control Systems Involving Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 793-811, June.
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