Laplace变换与分数阶中立型时滞微分方程Laplace Transform and Fractional-Order Neutral Delay Differential Equations
田垒,李琳,杨海洋
摘要(Abstract):
Laplace变换是求解整数阶线性微分方程的一种有效且方便的方法。本文主要应用Gronwall积分不等式获得Laplace变换法求解常系数分数阶中立型时滞微分方程合理性的条件。
关键词(KeyWords): Gronwall积分不等式;拉普拉斯变换;分数阶中立型微分方程;Caputo分数导数
基金项目(Foundation): 安徽省高等学校省级自然科学研究基金项目(KJ2011A197,KJ2013Z186)
作者(Author): 田垒,李琳,杨海洋
DOI: 10.13757/j.cnki.cn34-1150/n.2015.01.002
参考文献(References):
- [1]Miller K.S.,Ross B..An Introduction to the Fractional Calculus and Fractional Differential Equations[M].John Wiley&Sons,New York,1993.
- [2]Podlubny I.,Fractional Differential Equations[M].Academic Press,San Diego,1999.
- [3]Kilbas A.A.,Srivastava,H.M.,Trujillo J.J..Theory and Applications of Fractional Differential Equations[M].Elsevier Science B.V.,Amsterdam,The Netherlands,2006.
- [4]Diethelm K..The Analysis of Fractional Differential Equations[M].Springer-Verlag Berlin,Heidelberg,2010.
- [5]张海,郑祖庥,蒋威.非线性分数阶泛函微分方程解的存在性[J].数学物理学报,2011,31A(2):289–297.
- [6]张海,赵小文,蒋威.分数阶一般退化微分系统的通解[J].数学杂志,2011,31(1):91–95.
- [7]Lin S.D.,Lu C.H..Laplace transform for solving some families of fractional differential equations and its applications[J].Advances in Difference Equations,2013(137):1-9.
- [8]Zhang Hai,Cao Jinde,Jiang Wei,General solution of linear fractional neutral differential difference equations[J].Discrete Dynamics in Nature and Society,2013,Article ID 489521,1-7.
- [9]Li K.X.,Peng J.G.,Laplace transform and fractional differential equations[J].Applied Mathematics Letters,2011,24(12):2019–2023.
- [10]Hamdy M.A..Fractional neutral evolution equations with nonlocal conditions[J].Advances in Difference Equations,2013(117):1-10.
扩展功能
本文信息
服务与反馈
本文关键词相关文章
本文作者相关文章
中国知网
分享