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Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses

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  • Dhayal, Rajesh
  • Zhu, Quanxin

Abstract

This paper is devoted to exploring a new class of ψ-Hilfer fractional integro-differential systems under the influence of impulses. Using semigroup theory, fixed-point technique, and fractional calculus, we analyzed the existence and uniqueness of mild solutions. Moreover, we proved the novel stability criteria for the considered system by using the Grönwall inequality. Further, we investigated the controllability results for the proposed system by using the new piecewise control function. Finally, the main results are validated with the aid of an example.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000061
    DOI: 10.1016/j.chaos.2023.113105
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    References listed on IDEAS

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    1. Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
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    5. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Dhayal, Rajesh & Malik, Muslim, 2021. "Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. 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.
    8. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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