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,(03):189-194,217.
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
- Title:
- Existence of Lyapunov inequality and its solutions for a class of boundary value problems for fractional differential equations of Hardmard type
- 文章编号:
- 1004-4353(2023)03-0189-07
- 关键词:
- Hadamard型分数阶微分方程; Lyapunov不等式; 边值问题; 格林函数; 不动点定理
- Keywords:
- fractional differential equation of Hardmard type; Lyapunov inequation; boundary value problem; Green function; fixed point theorem
- 分类号:
- O175.8
- 文献标志码:
- A
- 摘要:
- 研究了一类Hadamard型分数阶微分方程的边值问题.首先,将微分方程边值问题转化为等价的积分方程问题; 其次,根据边值条件求出微分方程相应的格林函数,并利用格林函数的性质得出微分方程所对应的Lyapunov不等式; 最后,分别利用Banach压缩映像原理和Leray - Schauder不动点定理证明了该类非线性边值问题解的存在性,并通过算例验证了所得结果的正确性.
- Abstract:
- A Hadamard type boundary value problem for fractional differential equations was studied.Firstly, the boundary value problem of differential equation was equivalent to the integral equation problem.Secondly, the corresponding Green function was obtained according to the boundary value conditions, and the Lyapunov inequality corresponding to the equation was obtained by using the properties of Green function.Finally, the existence of solutions for a class of nonlinear boundary value problems was proved by Banach compression mapping principle and Leray - Schauder fixed point theorem respectively.The correctness of the results obtained in this paper was verified by an example.
参考文献/References:
[1] MA Q H, MA C, WANG J U.A Lyapunov - type inequality for a fractional differential equation with Hadamard derivative[J].Journal of Mathematical Inequalities, 2017,11(1):135 - 141.
[2] LAADJAL Z, ADJEROUD N, MA Q.Lyapunov - type inequality for the Hadamard fractional boundary value problem on a general interval [a,b][J].Journal of Mathematical Inequalities, 2019,13(3):789 - 799.
[3] 武杰慧,马德香.一类分数阶微分方程边值问题的Lyapunov不等式及其正解的存在性[J].汕头大学学报(自然科学版),2022,37(2):26 - 33.
[4] 张丽平.两类混合型分数阶微分方程的边值问题解的存在性研究[D].昆明:云南师范大学,2022.
[5] 郑春华,宁艳艳.一类分数阶Laplacian方程边值问题解的存在性与唯一性[J].云南民族大学学报(自然科学版),2014,23(6):429 - 433.
[6] 杨海鹏.Banach压缩映射原理的应用[J].湖南工程学院学报(自然科学版),2018,28(1):53 - 56.
[7] 甘亦苗,侯成敏.一类Hadamard型分数阶微分方程解的存在唯一性[J].延边大学学报(自然科学版),2021,47(2):95 - 100.
[8] 武杰慧.两类分数阶微分方程边值问题的Lyapunov不等式研究[D].北京:华北电力大学,2022.
[9] FERREIRA R A C.A Lyapunov - type inequality for a fractional boundary value problem[J].Fractional Calculus and Applied Analysis, 2013,16(4):978 - 984.
[10] OREGAN D, SAMET B.Lyapunov - type inequalities for a class of fractional differential equations[J].Journal of Inequalities and Applications, 2015,247(1):1 - 10.
相似文献/References:
[1]甘亦苗,侯成敏*.一类Hadamard型分数阶微分方程解的存在唯一性[J].延边大学学报(自然科学版),2021,47(02):95.
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[2]王枫,葛琦.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[J].延边大学学报(自然科学版),2023,(01):1.
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备注/Memo
收稿日期: 2023-04-28
第一作者: 葛月英(1999—),女,硕士研究生,研究方向为常微分方程理论及其应用.
通信作者: 葛琦(1975—),女,硕士,教授,研究方向为常微分方程理论及其应用.