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Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

Author

Listed:
  • Bashir Ahmad
  • Juan J. Nieto

Abstract

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional order given by , , , , ,  ,  , . Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.

Suggested Citation

  • Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
    • Handle: RePEc:hin:jnlaaa:494720
    DOI: 10.1155/2009/494720
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    Citations

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    Cited by:

    1. Jiqiang Jiang & Lishan Liu & Yonghong Wu, 2012. "Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann‐Stieltjes Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Yansheng Liu, 2013. "Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Azarnavid, Babak & Emamjomeh, Mahdi & Nabati, Mohammad, 2022. "A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Sotiris K. Ntouyas & Phollakrit Wongsantisuk & Ayub Samadi & Jessada Tariboon, 2024. "Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function," Mathematics, MDPI, vol. 12(7), pages 1-21, April.
    5. Lihong Zhang & Bashir Ahmad & Guotao Wang & Ravi P. Agarwal & Maryem Al-Yami & Wafa Shammakh, 2013. "Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Mujeeb Ur Rehman & Rahmat Ali Khan, 2010. "Positive Solutions to Nonlinear Higher‐Order Nonlocal Boundary Value Problems for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    7. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Min Jiang & Shouming Zhong, 2014. "Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    10. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    11. Meysam Alvan & Rahmat Darzi & Amin Mahmoodi, 2016. "Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 4(1), pages 1-10, March.
    12. Wen-Xue Zhou & Hai-Zhong Liu, 2012. "Existence of Weak Solutions for Nonlinear Fractional Differential Inclusion with Nonseparated Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    13. Yulin Zhao & Li Huang & Xuebin Wang & Xianyang Zhu, 2012. "Existence of Solutions for Fractional Integro‐Differential Equation with Multipoint Boundary Value Problem in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Liping Wang & Zongfu Zhou & Hui Zhou, 2014. "Positive Solutions for Singular p‐Laplacian Fractional Differential System with Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    15. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    16. N. I. Mahmudov & S. Unul, 2014. "Existence of Solutions of α ∈ (2,3] Order Fractional Three‐Point Boundary Value Problems with Integral Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    17. Jing Zhao & Peifen Lu & Yiliang Liu, 2013. "Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    18. Zeeshan Ali & Poom Kumam & Kamal Shah & Akbar Zada, 2019. "Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-26, April.

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