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Numerical Solutions for the Three‐Point Boundary Value Problem of Nonlinear Fractional Differential Equations

Author

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  • C. P. Zhang
  • J. Niu
  • Y. Z. Lin

Abstract

We present an efficient numerical scheme for solving three‐point boundary value problems of nonlinear fractional differential equation. The main idea of this method is to establish a favorable reproducing kernel space that satisfies the complex boundary conditions. Based on the properties of the new reproducing kernel space, the approximate solution is obtained by searching least value techniques. Moreover, uniformly convergence and error estimation are provided for our method. Numerical experiments are presented to illustrate the performance of the method and to confirm the theoretical results.

Suggested Citation

  • C. P. Zhang & J. Niu & Y. Z. Lin, 2012. "Numerical Solutions for the Three‐Point Boundary Value Problem of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:360631
    DOI: 10.1155/2012/360631
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    References listed on IDEAS

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    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    2. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
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    Cited by:

    1. 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).
    2. Jing Niu & Yingzhen Lin & Minggen Cui, 2013. "A Novel Approach to Calculation of Reproducing Kernel on Infinite Interval and Applications to Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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