一类含CFC-分数阶导数微分方程的Lyapunov不等式及其解的存在唯一性  

Lyapunov inequalities and existence and uniqueness of solutions for a class of differential equations with CFC-fractional derivatives

作　　者：王枫 葛琦[1] WANG Feng;GE Qi(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2023年第1期1-7,共7页Journal of Yanbian University（Natural Science Edition）

基　　金：吉林省教育厅科学技术研究项目(JJKH2022527KJ)。

摘　　要：研究了一类含CFC-分数阶导数的微分方程:(CFC_(0)D^(p)_(x))(t)+u(t)x(t)=0,2<p<3,0<t<1;x(0)=x'(0)=0,ax(1)+bx'(1)=0,a>0,b>0,0<b a<1.首先,分析了该方程所对应的格林函数的性质;其次,根据格林函数的性质得到了该微分方程的Lyapunov不等式;再次,将该类方程一般化,并利用Banach压缩映像原理建立了此类微分方程解的存在唯一性;最后,利用分数阶Gronwall不等式得到了微分方程(CFC_(0)D^(p)_(x))(t)+f(t,x(t))=0,2<p<3,0<t<1解的Hyers-Ulam稳定性.A class of fractional derivative differential equations with CFC is studied:(CFC_(0)D^(p)_(x))(t)+u(t)x(t)=0,2<p<3,0<t<1;x(0)=x'(0)=0,ax(1)+bx'(1)=0,a>0,b>0,0<b a<1.Firstly,the properties of the Green function corresponding to this kind of equation are analyzed,and then Lyapunov inequality for the kind of differential equation is obtained according to the properties of the Green function.Then,the kind of equation is generalized,and the existence and uniqueness of the solution of this kind of differential equation is established by using the Banach contraction mapping principle.Finally,the Hyers-Ulam stability of the solution of the differential equation(CFC_(0)D^(p)_(x))(t)+f(t,x(t))=0,2<p<3,0<t<1 is obtained by using the fractional Gronwall inequality.

关 键 词：CFC-分数阶导数 Lyapunov不等式 存在唯一性 分数阶Gronwall不等式 HYERS-ULAM稳定性 

分 类 号：O175[理学—数学]