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Periodic Boundary Value Problems for Fractional Dynamic Equations on Time Scales

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Abstract

The manuscript is concerned with the existence, uniqueness, and Ulam stability of solutions of a nonlinear fractional dynamic equation involving Caputo fractional nabla derivative with the periodic boundary conditions on time scales. Based on the fixed point theory, first, we investigate the existence of a solution and then employing dynamic inequality the uniqueness result is obtained. Next, we present several results on Ulam stability. An appropriate example has been given to demonstrate the implementation of theoretical results.

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Acknowledgements

The authors would like to thank the anonymous referees for their insightful comments and suggestions that significantly improved the quality of this manuscript.

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No funding was received for conducting this study.

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Authors and Affiliations

  1. Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh, Jote, Arunachal Pradesh,  791113 , India

    Bikash Gogoi & Utpal Kumar Saha

  2. Department of Mathematics, Gauhati University, Guwahati, Assam,  781014 , India

    Bipan Hazarika

  3. Department of Mathematics, Ramniranjan Jhunjhunwala College, Mumbai, Maharashtra,  400 086 , India

    Sanket Tikare

Authors
  1. Bikash Gogoi
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  2. Bipan Hazarika
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  3. Utpal Kumar Saha
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  4. Sanket Tikare
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All author’s contributed equally.

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Correspondence to Utpal Kumar Saha.

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Gogoi, B., Hazarika, B., Saha, U.K. et al. Periodic Boundary Value Problems for Fractional Dynamic Equations on Time Scales. Results Math 78, 228 (2023). https://doi.org/10.1007/s00025-023-02007-0

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  • DOI: https://doi.org/10.1007/s00025-023-02007-0

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