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Stability theory to a coupled system of nonlinear fractional hybrid differential equations

Author

Listed:
  • Samina

    (University of Malakand, Dir(L))

  • Kamal Shah

    (University of Malakand, Dir(L))

  • Rahmat Ali Khan

    (University of Malakand, Dir(L))

Abstract

In the current manuscript, we investigate existence of solutions to a coupled system of fractional hybrid differential equations (FHDEs). With the help of mixed type Lipschitz and Caratheodory conditions, some conditions for the existence of solutions to the considered problem are established. Considering the tools of nonlinear analysis and hybrid fixed points theory, we establish our results. Further some new type results about stability including Ulam-Hyers (UH), generalized Ulam-Hyers (GUH) stability, Ulam-Hyers-Rassias (UHR) and generalized Ulam-Hyers-Rassias (GUHR) stability are developed. A test problem is given to demonstrate the establish results.

Suggested Citation

  • Samina & Kamal Shah & Rahmat Ali Khan, 2020. "Stability theory to a coupled system of nonlinear fractional hybrid differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 669-687, June.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0423-7
    DOI: 10.1007/s13226-020-0423-7
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    References listed on IDEAS

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    1. Zada, Akbar & Shah, Omar & Shah, Rahim, 2015. "Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 512-518.
    2. 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.
    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.
    4. Mohamed A. E. Herzallah & Dumitru Baleanu, 2014. "On Fractional Order Hybrid Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
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