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Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations

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  • Muhammad Iqbal
  • Yongjin Li
  • Kamal Shah
  • Rahmat Ali Khan

Abstract

We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: , , , , , , , , , where , is linear, is Caputo fractional derivative of order , with , , and is fractional integral of order . The nonlinear functions , are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:7676814
    DOI: 10.1155/2017/7676814
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    References listed on IDEAS

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    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. 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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