WANG Feng,GE Qi.Lyapunov inequalities and existence and uniqueness of solutions for a class of differential equations with CFC - fractional derivatives[J].Journal of Yanbian University,2023,(01):1-7.
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
- Title:
- Lyapunov inequalities and existence and uniqueness of solutions for a class of differential equations with CFC - fractional derivatives
- 文章编号:
- 1004-4353(2023)01-0001-07
- Keywords:
- CFC - fractional derivative; Lyapunov inequality; existence and uniqueness; fractional Gronwall inequality; Hyers - Ulam stability
- 分类号:
- O175.8
- 文献标志码:
- A
- 摘要:
- 研究了一类含CFC - 分数阶导数的微分方程:{(CFC0Dpx)(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(CFC0Dpx)(t)+f(t,x(t))=0, 2<p<3, 0<t<1解的Hyers - Ulam 稳定性.
- Abstract:
- A class of fractional derivative differential equations with CFC is studied:{(CFC0Dpx)(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(CFC0Dpx)(t)+f(t,x(t))= 0, 2<p<3, 0<t<1 is obtained by using the fractional Gronwall inequality.
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相似文献/References:
[1]葛月英,葛琦.一类Hadamard型分数阶微分方程边值问题的Lyapunov不等式及其解的存在性[J].延边大学学报(自然科学版),2023,(03):189.
GE Yueying,GE Qi.Existence of Lyapunov inequality and its solutions for a class of boundary value problems for fractional differential equations of Hardmard type[J].Journal of Yanbian University,2023,(01):189.
备注/Memo
收稿日期: 2022-12-21
基金项目: 吉林省教育厅科学技术研究项目(JJKH2022527KJ)
第一作者: 王枫(1997—),男,硕士研究生,研究方向为常微分方程.
通信作者: 葛琦(1975—),女,硕士,教授,研究方向为常微分方程.