摘要
研究了一类具有Caputo导数的分数阶脉冲微分方程组的Fredholm边值问题,以及对应的弱扰动线性边值问题.其中边值问题由线性向量泛函指定,其分量的个数与分数阶脉冲微分方程组的维数不相等.通过求解相关齐次系统的通解和非齐次系统的任意一个特解,得出该分数阶微分方程组的通解.基于此通解,应用投影理论,构造出该边值问题的一类线性无关解.同时,在齐次生成边值问题的解不唯一且非齐次生成边值问题无解的条件下,确定了弱扰动线性边值问题解的分岔条件.最后,给出一个具体实例来说明主要结论的有效性.
This paper investigated the Fredholm boundary value problems for a class of fractional impulsive differential equation systems with Caputo derivatives,as well as the corresponding weakly perturbed linear boundary value problems.The boundary conditions were defined by linear vector functionals whose number of components did not equal the dimension of the fractional impulsive differential equation system.By solving the general solution of the associated homogeneous system and a particular solution of the nonhomogeneous system,the general solution of the fractional differential equation system was derived.Based on this general solution,a class of linearly independent solutions for the boundary value problem was constructed using projection theory.Furthermore,bifurcation conditions for solutions of the weakly perturbed linear boundary value problem were established under the circumstances where the homogeneous boundary value problem admitted non-unique solutions and the nonhomogeneous problem was unsolvable.Finally,a concrete example was provided to illustrate the validity of the main conclusions.
作者
刘龙
吴克晴
王慧慧
LIU Long;WU Keqing;WANG Huihui(College of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)
出处
《杭州师范大学学报(自然科学版)》
2025年第5期493-502,共10页
Journal of Hangzhou Normal University(Natural Science Edition)
基金
国家自然科学基金项目(12461010)。
关键词
边值问题
分数阶微分方程
脉冲
广义逆矩阵
分岔
boundary value problem
fractional differential equation
impulse
generalized inverse matrix
bifurcation
