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Hyers–Ulam stability and existence of solutions for high-order fractional q-difference equations on infinite intervals

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Abstract

Recently, fractional q-difference equations on infinite intervals have attracted much attention due to their potential applications in many fields. In this paper, we investigate a class of nonlinear high-order fractional q-difference equations with integral boundary conditions on infinite intervals, where the nonlinearity contains Riemann–Liouville fractional q-derivatives of different orders of unknown function. By means of Schaefer fixed point theorem, Leray–Schauder nonlinear alternative and Banach contraction mapping principle, we acquire the existence and uniqueness results of solutions. Furthermore, we establish the Hyers–Ulam stability for the proposed problem. In the end, several concrete examples are utilized to demonstrate the validity of main results.

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions. The research project is supported by the Natural Science Foundation of Hebei Province (Grant No. A2015208114) and the Foundation of Hebei Education Department (Grant No. QN2017063).

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Author notes

  1. Jufang Wang, Jinye Zhang and Changlong Yu contributed equally to this work.

Authors and Affiliations

  1. College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, China

    Jufang Wang, Jinye Zhang & Changlong Yu

  2. Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Changlong Yu

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  1. Jufang Wang
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  2. Jinye Zhang
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  3. Changlong Yu
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Correspondence to Changlong Yu.

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Wang, J., Zhang, J. & Yu, C. Hyers–Ulam stability and existence of solutions for high-order fractional q-difference equations on infinite intervals. J. Appl. Math. Comput. 69, 4665–4688 (2023). https://doi.org/10.1007/s12190-023-01947-8

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  • DOI: https://doi.org/10.1007/s12190-023-01947-8

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