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Existence of Positive Solutions for m‐Point Boundary Value Problem for Nonlinear Fractional Differential Equation

Author

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  • Moustafa El-Shahed
  • Wafa M. Shammakh

Abstract

We investigate an m‐point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett‐Williams fixed point theorem, the existence of multiple positive solutions is obtained.

Suggested Citation

  • Moustafa El-Shahed & Wafa M. Shammakh, 2011. "Existence of Positive Solutions for m‐Point Boundary Value Problem for Nonlinear Fractional Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:986575
    DOI: 10.1155/2011/986575
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    Cited by:

    1. 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.
    2. Kamal Shah & Poom Kumam & Inam Ullah, 2019. "On Ulam Stability and Multiplicity Results to a Nonlinear Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    3. Chen Yang & Xiaolin Zhu, 2020. "Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p‐Laplacian Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).

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