Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

doi:10.1088/1674-1056/19/5/050203

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50203-050203.doi: 10.1088/1674-1056/19/5/050203

Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

石兰芳¹, 莫嘉琪²

(1)College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China;College of Sciences, Hohai University, Nanjing 210098, China; (2)Department of Mathematics, Anhui Normal University, Wuhu 241000, China

收稿日期:2009-07-23 修回日期:2009-08-14 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
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).

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, China^b College of Sciences, Hohai University, Nanjing 210098, China; ^c Department of Mathematics, Anhui Normal University, Wuhu 241000, China

Received:2009-07-23 Revised:2009-08-14 Online:2010-05-15 Published:2010-05-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: semilinear, fractional differential equation, singular perturbation

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

02.30.Mv (Approximations and expansions)

石兰芳, 莫嘉琪. Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation[J]. 中国物理B, 2010, 19(5): 50203-050203.

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[J]. Chin. Phys. B, 2010, 19(5): 50203-050203.

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Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

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