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On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Author

Listed:
  • Jiraporn Reunsumrit

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

Abstract

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

Suggested Citation

  • Jiraporn Reunsumrit & Thanin Sitthiwirattham, 2020. "On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations," Mathematics, MDPI, vol. 8(4), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:476-:d:339347
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    References listed on IDEAS

    as
    1. Thabet Abdeljawad, 2013. "On Delta and Nabla Caputo Fractional Differences and Dual Identities," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, July.
    2. 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.
    3. Thabet Abdeljawad & Ferhan M. Atici, 2012. "On the Definitions of Nabla Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-13, October.
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