| 谢宇,周凤英.一种新的小波方法求解一类分数阶微分方程[J].井冈山大学自然版,2020,41(3):1-8 |
| 一种新的小波方法求解一类分数阶微分方程 |
| A New Wavelet Method for Solving A Class of Fractional Differential Equations |
| 投稿时间：2019-11-29 修订日期：2020-04-10 |
| DOI：10.3969/j.issn.1674-8085.2020.03.001 |
| 中文关键词: 第五类Chebyshev小波 Block Pulse函数 分数阶积分算子 收敛性分析 分数阶微分方程 |
| 英文关键词: the fifth kind Chebyshev wavelet Block Pulse function fractional integral operator convergence analysis fractional differential equation |
| 基金项目:国家自然科学基金项目（11601076）；东华理工大学博士科研启动基金项目（DHBK2019213） |
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| 中文摘要: |
| 通过对第五类Chebyshev多项式进行伸缩平移，构造了第五类Chebyshev小波。利用Block Pulse函数近似第五类Chebyshev小波求得其分数阶积分算子。由第五类Chebyshev多项式的性质证明了该小波级数的收敛性，并给出小波逼近函数的截断误差估计。此外，将第五类Chebyshev小波应用于分数阶微分方程的求解，通过数值算例，验证了该方法的有效性。 |
| 英文摘要: |
| The fifth kind Chebyshev wavelet is constructed by stretching and translating the fifth kind Chebyshev polynomials. The Block Pulse function is used to approximate the fifth kind Chebyshev wavelet to obtain its fractional integration operator. The convergence of the wavelet series is proved by the property of the fifth Chebyshev polynomial, and the truncation error estimation of the wavelet approximating function is given. In addition, the fifth kind Chebyshev wavelet is applied to solve fractional differential equations, and numerical examples are given for verifying the effectiveness of the method. |
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