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Shock wave solution for a class of nonlinear nonlocal singularly perturbed fractional differential equation

  • Mathematics
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

A class of boundary value problems for the nonlinear nonlocal singularly perturbed fractional differential equation is considered. Firstly, the outer solution of the original problem is obtained. Secondly, by using the stretched variables and the composing expansion method, the shock wave layer and boundary layers are constructed. Finally, by using the theory of differential inequality, the asymptotic behavior of solution for the original boundary value problem of nonlinear nonlocal singularly perturbed fractional differential equation is studied. And the uniformly valid asymptotic estimation is discussed.

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Authors and Affiliations

  1. Department of Basic Teaching, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu 241002, Anhui, China

    Juanrong Shi

  2. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China

    Juanrong Shi

  3. Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui, China

    Jiaqi Mo

Authors
  1. Juanrong Shi
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  2. Jiaqi Mo
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Correspondence to Jiaqi Mo.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (40676016), the Natural Science Foundation of the Education Department of Anhui Province (KJ2015A418)

Biography: SHI Juanrong, female, Master, Associate professor, research direction: applied mathematics.

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Shi, J., Mo, J. Shock wave solution for a class of nonlinear nonlocal singularly perturbed fractional differential equation. Wuhan Univ. J. Nat. Sci. 22, 13–18 (2017). https://doi.org/10.1007/s11859-017-1211-z

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  • DOI: https://doi.org/10.1007/s11859-017-1211-z

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