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Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions

Author

Listed:
  • Xiping Liu
  • Fanfan Li
  • Mei Jia
  • Ertao Zhi

Abstract

We study the existence and uniqueness of the solutions for the boundary value problem of fractional differential equations with nonlinear boundary conditions. By using the upper and lower solutions method in reverse order and monotone iterative techniques, we obtain the sufficient conditions of both the existence of the maximal and minimal solutions between an upper solution and a lower solution and the uniqueness of the solutions for the boundary value problem and present the iterative sequence for calculating the approximate analytical solutions of the boundary value problem and the error estimate. An example is also given to illustrate the main results.

Suggested Citation

  • Xiping Liu & Fanfan Li & Mei Jia & Ertao Zhi, 2014. "Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:758390
    DOI: 10.1155/2014/758390
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    References listed on IDEAS

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    1. Mei Jia & Xiping Liu, 2014. "The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jia, Mei & Liu, Xiping, 2014. "Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 313-323.
    3. Mei Jia & Xiping Liu, 2014. "The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, March.
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