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Existence Results To A Class Of Hybrid Fractional Differential Equations

Author

Listed:
  • Zakir Ullah

    (Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan.)

  • Amjad Ali

    (Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan.)

  • Rahmat Ali Khan

    (Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan.)

  • Muhammad Iqbal

    (Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan.)

Abstract

This article is devoted to the study of existence results to a class of boundary value problems for hybrid fractional differential equations. A couple of hybrid fixed point theorems for the sum of three operators are used for proving the main results. Examples illustrating the results are also presented.

Suggested Citation

  • Zakir Ullah & Amjad Ali & Rahmat Ali Khan & Muhammad Iqbal, 2018. "Existence Results To A Class Of Hybrid Fractional Differential Equations," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 13-17, January.
    • Handle: RePEc:zib:zbmsmk:v:2:y:2018:i:1:p:13-17
    DOI: 10.26480/msmk.01.2018.13.17
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    References listed on IDEAS

    as
    1. Gao, Lijun & Wang, Dandan & Wang, Gang, 2015. "Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 186-200.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. 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.
    4. 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.
    5. Mohamed A. E. Herzallah & Dumitru Baleanu, 2014. "On Fractional Order Hybrid Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    6. Wang, JinRong & Li, Xuezhu, 2015. "Ulam–Hyers stability of fractional Langevin equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 72-83.
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    Cited by:

    1. 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.

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