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Positive solutions of three-point fractional sum boundary value problem for Caputo fractional difference equations via an argument with a shift

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Abstract

In this paper, we study a new class of three-point boundary value problem of nonlinear Caputo fractional difference equation. Our problem contain an argument with a shift. The existence of at least one positive solution is proved by using the Guo-Krasnoselskii’s fixed point theorem. Some illustrative examples are given.

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Acknowledgments

This research was funded by King Mongkut’s University of Technology North Bangkok. Contract no. KMUTNB-GOV-58-51.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Applied Science, Nonlinear Dynamic Analysis Research Center, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

    Jiraporn Reunsumrit & Thanin Sitthiwirattham

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  1. Jiraporn Reunsumrit
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  2. Thanin Sitthiwirattham
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Correspondence to Thanin Sitthiwirattham.

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Reunsumrit, J., Sitthiwirattham, T. Positive solutions of three-point fractional sum boundary value problem for Caputo fractional difference equations via an argument with a shift. Positivity 20, 861–876 (2016). https://doi.org/10.1007/s11117-015-0391-z

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  • DOI: https://doi.org/10.1007/s11117-015-0391-z

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