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Existence and Stability Analysis for Fractional Impulsive Caputo Difference-Sum Equations with Periodic Boundary Condition

Author

Listed:
  • Rujira Ouncharoen

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Saowaluck Chasreechai

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand)

Abstract

In this paper, by using the Banach contraction principle and the Schauder’s fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:843-:d:361961
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    References listed on IDEAS

    as
    1. Yanli Chen & Yongxiang Li, 2014. "The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, August.
    2. 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.
    3. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
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