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On Nonlinear Fractional Sum-Difference Equations via Fractional Sum Boundary Conditions Involving Different Orders

Author

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  • Saowaluk Chasreechai
  • Chanakarn Kiataramkul
  • Thanin Sitthiwirattham

Abstract

We study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results.

Suggested Citation

  • Saowaluk Chasreechai & Chanakarn Kiataramkul & Thanin Sitthiwirattham, 2015. "On Nonlinear Fractional Sum-Difference Equations via Fractional Sum Boundary Conditions Involving Different Orders," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, November.
    • Handle: RePEc:hin:jnlmpe:519072
    DOI: 10.1155/2015/519072
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    Cited by:

    1. Rujira Ouncharoen & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2020. "Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    2. Jarunee Soontharanon & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    3. Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "On Separate Fractional Sum-Difference Equations with n -Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders," Mathematics, MDPI, vol. 7(5), pages 1-16, May.

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