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New existence and stability results for fractional Langevin equation with three-point boundary conditions

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Abstract

The aim of the paper is to present a new technical analysis of the special case of the nonlinear Langevin equation with positive friction constant involving two fractional orders with three-point boundary conditions. Using some basic properties of the special case of the Prabhakar integral operator, we find an equivalent integral equation to the mentioned equation. We obtain a new result on existence, uniqueness and Hyers–Ulam stability by employing contraction mapping principle and Krasnoselskii’s fixed point theorem with respect to an appropriate weighted Banach space. Our result is an improvement of existing results reported in the previous literature. The consistency of the main results is demonstrated by some examples.

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Acknowledgements

The authors are thankful to the Editor(s) and reviewers of the manuscript for their helpful comments. The work of H. Fazli and H. Sun was supported by the National Natural Science Foundation of China (11972148), Natural Science Foundation of Jiangsu Province (BK20190024), the Fundamental Research Funds for the Central Universities (2019B16014). The research of Juan J. Nieto has been partially supported by the Agencia Estatal de Investigacin (AEI) of Spain, cofinanced by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P; and by Xunta de Galicia under Grant ED431C 2019/02.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing, 210098, Jiangsu, China

    Hossein Fazli & HongGuang Sun

  2. Department of Statistics, Mathematical Analysis and Optimization, Institute of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

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  1. Hossein Fazli
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  2. HongGuang Sun
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  3. Juan J. Nieto
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Correspondence to HongGuang Sun.

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Communicated by Agnieszka Malinowska.

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Fazli, H., Sun, H. & Nieto, J.J. New existence and stability results for fractional Langevin equation with three-point boundary conditions. Comp. Appl. Math. 40, 48 (2021). https://doi.org/10.1007/s40314-020-01411-4

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  • DOI: https://doi.org/10.1007/s40314-020-01411-4

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