基于Caputo导数的Miller-Ross序列导数微分方程的稳定性分析  

Stability Analysis of Fractional Differential Equations with Miller-Ross Sequential Derivative in Caputo Sense

作　　者：钱德亮[1] 李常品[2] 

机构地区：[1]中原工学院数学系,河南郑州450007 [2]上海大学数学系,上海200444

出　　处：《数学的实践与认识》2012年第10期133-139,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10872119);上海大学研究生创新基金(SHUCX091046);上海市第三批重点学科(S30104);河南省自然科学基金(112300410022)

摘　　要：讨论了基于Caputo导数的Miller-Ross序列导数的分数阶微分方程的稳定性.根据Laplace变换,得到分数阶微分方程的解;应用Mittag-Leffler函数的渐近展开,讨论了方程的稳定性.分两部分:齐次方程与非齐次方程.Stability analysis of the linear fractional differential systems with Caputo derivative has been well-studied,the differential system with Miller-Ross sequential derivative in Caputo sense,however,has not been investigated yet.In this paper,by using the Laplace transform and the asymptotical expansion of the Mittag-Leffler function,we derive the stability criteria of the fractional differential systems with Miller-Ross sequential fractional derivative in Caputo sense,where two cases are included：the homogenous case and the non-homogenous one.

关 键 词：CAPUTO分数阶导数 Miller-Ross序列导数 Mittag-Leffler函数 稳定性 

分 类 号：O175[理学—数学]