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分数阶微分方程的Hyers-Ulam稳定性
发表时间：2016-01-15 浏览量：2544 下载量：1125
| 全部作者： | 郑安利，冯育强，王蔚敏 |
| 作者单位： | 武汉科技大学理学院 |
| 摘 要： | 在分数阶情形下，研究微分方程的Hyers-Ulam稳定性。对具有 Caputo导数的分数阶线性微分方程运用Laplace变换进行求解，再对其Hyers-Ulam稳定性进行讨论。对于非线性的情形，由于不能直接求出相应的解，而是用Volterra方程给出解析解的表达方式，然后利用分数阶Gronwall不等式的性质和不等式的放缩法讨论方程的Hyers-Ulam稳定性，得到相应的K值。 |
| 关 键 词： | 常微分方程；分数阶微分方程；Hyers-Ulam稳定性；分数阶Gronwall不等式；Laplace变换 |
| Title： | Hyers-Ulam stability of fractional differential equations |
| Author： | ZHENG Anli, FENG Yuqiang, WANG Weimin |
| Organization： | College of Science, Wuhan University of Science and Technology |
| Abstract： | This paper studies the Hyers-Ulam stability of fractional differential equations. The fractional differential equation with Caputo’s derivative is solved by applying Laplace transform, and then its Hyers-Ulam stability is discussed. As for nonlinear condition, due to that the corresponding solution can not be directly found, the expression of the analytical solutions is given by Volterra equations. The conclusion of Hyers-Ulam stability is drawn via fractional Gronwall inequality and scaling of inequality to give the corresponding K values. |
| Key words： | ordinary differential equation; fractional differential equation; Hyers-Ulam stability; fractional Gronwall inequality; Laplace transform |
| 发表期数： | 2016年1月第1期 |
| 引用格式： | 郑安利，冯育强，王蔚敏. 分数阶微分方程的Hyers-Ulam稳定性[J]. 中国科技论文在线精品论文，2016，9（1）：63-70. |
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