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Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation |
| Shi Lan-Fang(石兰芳)a)b)† and Mo Jia-Qi(莫嘉琪)c) |
| a College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, Chinab College of Sciences, Hohai University, Nanjing 210098, China; c Department of Mathematics, Anhui Normal University, Wuhu 241000, China |
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Abstract This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation. Under the suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, using the stretched variable and the composing expansion method the boundary layer is constructed; finally, using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed.
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Received: 23 July 2009
Revised: 14 August 2009
Accepted manuscript online:
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PACS:
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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02.30.Mv
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(Approximations and expansions)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~40676016 and 40876010), the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No.~KZCX2-YW-Q03-08), LASG State Key Laboratory Special Fund and R$&$D Special Fund for Public Welfare Industry (meteorology) (Grant No.~GYHY200806010). |
Cite this article:
Shi Lan-Fang(石兰芳) and Mo Jia-Qi(莫嘉琪) Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation 2010 Chin. Phys. B 19 050203
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