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On stability analysis of hybrid fractional boundary value problem

Author

Listed:
  • Vidushi Gupta

    (Chandigarh University)

  • Arshad Ali

    (University of Malakand)

  • Kamal Shah

    (University of Malakand)

  • Syed Abbas

    (Indian Institute of Technology Mandi)

Abstract

The novelty of the present article is to introduce the study of hybrid dynamical system of order $$\xi \in (\delta -1,\delta ]$$ ξ ∈ ( δ - 1 , δ ] with finite time delay. These hybrid systems are more suitable to deal several dynamical process as particular cases. The importance of this manuscript is to discuss the concept of stability results including Ulam-Hyers stability (UHS), generalized Ulam-Hyers stability (GUHS), Ulam-Hyers Rassias stability (UHRS) and generalized Ulam-Hyers Rassias stability (GUHRS). Meanwhile, we investigate some sufficient conditions for existence result of the solution for proposed work by adopting the application of fixed point theorem of Banach algebra due to Dhage under mixed Lipschitz and Carathéodory conditions. Finally the paper is enriched by two interesting applications to demonstrate our results.

Suggested Citation

  • Vidushi Gupta & Arshad Ali & Kamal Shah & Syed Abbas, 2021. "On stability analysis of hybrid fractional boundary value problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 27-38, March.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:1:d:10.1007_s13226-021-00133-5
    DOI: 10.1007/s13226-021-00133-5
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    References listed on IDEAS

    as
    1. Shah, Kamal & Khalil, Hammad & Khan, Rahmat Ali, 2015. "Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 240-246.
    2. Zidane Baitiche & Kaddour Guerbati & Mouffak Benchohra & Yong Zhou, 2019. "Boundary Value Problems for Hybrid Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 7(3), pages 1-11, March.
    3. Khalil, Hammad & Khan, Rahmat Ali & Shah, Kamal, 2015. "Corrigendum to “Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations” [Chaos, Solitons & Fractals Volume 77," Chaos, Solitons & Fractals, Elsevier, vol. 78(C), pages 329-330.
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