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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions

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  • Thanin Sitthiwirattham
  • Jessada Tariboon
  • Sotiris K. Ntouyas

Abstract

We consider a discrete fractional boundary value problem of the form where , , , and is a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnddns:104276
    DOI: 10.1155/2013/104276
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    References listed on IDEAS

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    1. 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.
    2. A. Guezane-Lakoud & R. Khaldi, 2012. "Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-13, July.
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