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Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations

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  • Shah, Kamal
  • Khalil, Hammad
  • Khan, Rahmat Ali

Abstract

In this article, we study a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions. We use the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem for uniqueness and existence results. As in application, we provide an example to illustrate our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:77:y:2015:i:c:p:240-246
    DOI: 10.1016/j.chaos.2015.06.008
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    References listed on IDEAS

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    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
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    Cited by:

    1. Hamdi Gassara & Dhouha Kharrat & Abdellatif Ben Makhlouf & Lassaad Mchiri & Mohamed Rhaima, 2023. "SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System," Mathematics, MDPI, vol. 11(13), pages 1-10, July.
    2. 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.
    3. 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.
    4. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    5. 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.
    6. Mohamed Hannabou & Hilal Khalid, 2019. "Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-9, December.
    7. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    8. Ghulam Hussain & Rahmat Ali Khan, 2018. "Existence Of Solution To A Boundary Value Problem Of Hybrid Fractio nal Differential Equations Using Degree Method," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 24-28, January.
    9. Muhammad Shoaib & Kamal Shah & Rahmat Ali Khan, 2017. "On Applications Of Coupled Fixed -Point Theorem In Hybrid Differential Equations Of Arbitrary Order," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 1(2), pages 17-21, November.
    10. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    11. Muhammad Iqbal & Yongjin Li & Kamal Shah & Rahmat Ali Khan, 2017. "Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations," Complexity, Hindawi, vol. 2017, pages 1-9, July.

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