LAPLACE TRANSFORM OF FRACTIONAL ORDER DIFFERENTIAL EQUATIONS

被引：0
|
作者：
Liang, Song [1 ]
Wu, Ranchao [1 ]
Chen, Liping [2 ]
机构：
[1] Anhui Univ, Sch Math, Hefei 230601, Peoples R China
[2] Hefei Univ Technol, Sch Elect Engn & Automat, Hefei 230009, Peoples R China
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年
基金：
美国国家科学基金会; 高等学校博士学科点专项科研基金;
关键词：
Fractional-order differential equation; Laplace transform; exponential order; NEURAL-NETWORKS; DELAY SYSTEMS; TIME-DELAYS; STABILITY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Holder inequalities. They are showed be to of exponential order, which are necessary to apply the Laplace transform. Based on the estimates of solutions, the fractional-order and the integer-order derivatives of solutions are all estimated to be exponential order. As a result, the Laplace transform is proved to be valid in fractional equations.
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页数：15
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