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

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。

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.