| 摘要: |
| 这篇文章讨论了一类带阻尼项的分数阶偏微分方程在 Robin边界条件下的强迫振动性。首先利用积分平均值方法，分数阶偏微分方程的强迫振动性转化为了分数阶常微分不等式正解的存在性问题。
然后，根据 Riemann-Liouville微积分的一些特殊性质和不等式技巧，得到了强迫振动新的准则。最后给出了两个例子用以说明结论的正确性。 |
| 关键词: 分数阶偏微分方程，强迫振动，Riemann-Liouville分数阶微积分 |
| DOI： |
| 分类号:35B05,35R11,34K37 |
| 基金项目: |
|
| Forced Oscillation of Fractional Partial Differential Equations with Damping Term |
|
ma qingxia,Liu Anping
|
|
School of Mathematics and Physics, China University of Geosciences, Wuhan
|
| Abstract: |
| In this paper, we study the forced oscillation theory of a
fractional partial differential equation with damping term subject to Robin boundary condition.
By an integration average technique, the forced oscillation of the fractional partial differential
equation is transformed into the existence of eventually positive solutions of a fractional ordinary differential inequality.
Then based on the properties of the Riemann-Liouville calculus and inequalities,
some new oscillation criteria for the fractional partial differential equations are obtained.
Two examples are given to show the applications of our main results. |
| Key words: fractional partial differential equations, forced oscillation, Riemann-Liouville fractional calculus |
