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On Separate Fractional Sum-Difference Equations with n -Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders

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  • 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 10700, Thailand)

Abstract

In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder’s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:471-:d:234135
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    References listed on IDEAS

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    1. 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.
    2. Saowaluck Chasreechai & Thanin Sitthiwirattham, 2018. "Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, January.
    3. 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.
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