一类分数阶微分方程的比较定理与应用  

A Class of Comparison Theorems and Application of Fractional Differential Equation

作　　者：滕兴虎 毛自森 李静 韩笑 TENG Xing-hu;MAO Zi-sen;LI Jing;HAN Xiao(Department of General Education, Army Engineering University of PLA, Nanjing 211101, China)

机构地区：[1]中国人民解放军陆军工程大学基础部,南京211101

出　　处：《西南师范大学学报（自然科学版）》2021年第5期1-7,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12072370).

摘　　要：利用分数阶微分方程与相应的Volterra积分方程的等价性以及广义积分中值定理,给出了一类分数阶比较定理新的证明并进行了推广.利用比较定理研究了一类分数阶微分方程解的稳定性.By the equivalence of fractional differential equations and the corresponding Volterra integral equation,and with the mean value theorem for improper integral,a new proof of comparison theorem of fractional differential equation is given.And the comparison theorems are generalized.Also,the stability of a kind of fractional differential equation is discussed with the comparison theorem.And examples are given to illustrate the results.

关 键 词：分数阶微分方程 比较定理 VOLTERRA积分方程 稳定性 分数阶松弛振荡方程 

分 类 号：O175.1[理学—数学]