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Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations

Author

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  • Jinhua Wang
  • Hongjun Xiang
  • Zhigang Liu

Abstract

We consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solution are obtained. Two examples are given to demonstrate the feasibility of the obtained results.

Suggested Citation

  • Jinhua Wang & Hongjun Xiang & Zhigang Liu, 2010. "Positive Solution to Nonzero Boundary Values Problem for a Coupled System of Nonlinear Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-12, July.
    • Handle: RePEc:hin:jnijde:186928
    DOI: 10.1155/2010/186928
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    Cited by:

    1. Wen-Xue Zhou & Hai-zhong Liu, 2014. "Uniqueness and Existence of Solution for a System of Fractional q‐Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Fuquan Jiang & Xiaojie Xu & Zhongwei Cao, 2013. "The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Abdullahi, Auwal, 2021. "Modelling of transmission and control of Lassa fever via Caputo fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Thanin Sitthiwirattham & Jessada Tariboon & Sotiris K. Ntouyas, 2013. "Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, September.
    5. 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).
    6. Ying Wang & Lishan Liu & Xinguang Zhang & Yonghong Wu, 2014. "Positive Solutions for (n − 1,1)‐Type Singular Fractional Differential System with Coupled Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Payam Nasertayoob & S. Mansour Vaezpour & Dumitru Baleanu, 2014. "Solvability for a Coupled System of Fractional Integrodifferential Equations with m‐Point Boundary Conditions on the Half‐Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. 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).

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