摘要
随着分数阶微分方程在各个研究领域的广泛应用,分数阶微分方程的理论研究引起了国内外学者们的广泛关注。文章研究了分数阶中立型时滞微分方程在Caputo导数意义下解的存在唯一问题以及通解表达式。首先利用分步法分析了分数阶中立型时滞微分方程的解的存在唯一的条件;其次在保证解存在的前提下,通过构造基础解系,利用Laplace变换给出了分数阶中立型时滞微分方程的通解表达式。
Many scholars pay much attention to fractional differential equation with time delay because it plays an important role in many fields. This paper deals with the existence and uniqueness of the so- lution of fractional neutral differential equation with time delay based on Caputo de!：ivative and its gen- eral representation. Firstly, by the method of step by step, the conditions for the existence and u- niqueness of the solution of fractional neutral differential equation with time delay are analyzed. Then in the condition of the existence of the solution, the general representation is given by defining the basic solution and using Laplace transformation.
出处
《合肥工业大学学报（自然科学版）》
CAS
北大核心
2017年第9期1294-1296,共3页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(11371027
11471015
11601003)
高等学校博士点专项科研基金资助项目(20123401120001)
安徽省自然科学基金资助项目(1608085MA12)
安徽大学博士科研启动经费资助项目(023033190142)
安徽大学研究生学术创新研究扶持与强化资助项目(yfc10013)
关键词
分数阶
时滞
中立型微分方程
解的存在性
通解
fractional order
time delay
neutral differential equation
existence of solution
general solution
