摘要
研究一类含时间分数阶导数的热传导与膜振动问题,该问题边界正弦摄动变化。首先对边界自变量运用泰勒级数展开,使小参数只影响边界,不影响自变量;然后引入多重尺度到原方程及边界,得到关于小参数的零次幂和一次幂方程,获得热传导与膜振动问题关于小参数零次幂近似解。利用Riemann-Liouville分数阶导数和积分的定义与性质,分别讨论热传导与膜振动问题的解的变化规律,探讨了热传导与膜振动问题中分数阶导数对原问题解的影响。
Solutions of a class of the membrane vibration and heat conduction problems with time fractional derivative and sine-waving on the boundary were studied.Firstly,the Taylor series is employed to expand independent variables of the boundary,so that the small parameter only affect the boundary but independent variables.Then multiple scales were introduced into the original equation and the boundary,the equations on the 0 power of small parameter and the 1 power of small parameter were developed.The approximate solution of the equations of the membrane vibration problem and the heat conduction problem about the 0 power of small parameter were obtained.With the definition and properties of Riemann-Liouville fractional derivative and fractional integration,the change rules of the solutions of the membrane vibration problem and the heat conduction problem were discussed,respectively.The effects from fractional derivative of the membrane vibration problem and the heat conduction problem on the original problem were developed.
作者
慕文
李春源
葛志新
MUWen;LI Chunyuan;GE Zhixin(School of Mathematics&Physics Science and Engineering,Anhui University of Technology,Ma’anshan 243032,China)
出处
《安徽工业大学学报（自然科学版）》
CAS
2019年第2期190-194,共5页
Journal of Anhui University of Technology（Natural Science）
基金
安徽省高校自然科学研究重点项目(KJ2016A084)
安徽工业大学大学生创新创业训练计划项目(省级)(201810360367)
关键词
多重尺度
时间分数阶导数
可解性条件
multiple scales
time fractional derivative
solvable condition
