小波算子矩阵法求分数阶积分与微分近似值  

Wavelet operational matrix method for solving approximations of fractional integrals and fractional derivatives

作　　者：彭超[1] 宋向东[1] 仪明旭[1] 魏金侠[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第2期285-288,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：全国统计科研计划基金资助项目(2011LY064)

摘　　要：计算一类函数分数阶积分及其Caputo分数阶微分的问题.采用Haar小波和算子矩阵相结合的方法,得到一种Haar小波分数阶积分算子矩阵,利用该算子矩阵,对给定函数做了有效的离散,充分结合Haar小波矩阵的正交性、稀疏性,将求分数阶微积分问题转化为算子矩阵的乘积,从而便于计算机求解.平稳信号和非平稳信号的数值算例验证了该方法的可行性和有效性.In this paper, Haar wavelet operational matrix of fractional order integration is given oy comommg Haar wavelet with operational matrix. The operational matrix of fractional order integration is utilized to calculate fractional integrals and Caputo fractional derivatives of a class of functions. The authors transform the problem of solving fractional integrals and derivatives into the multiplication of the operational matrix, therefore the computation becomes convenient. Finally the numerical examples show that the method presented in this paper is feasible and effective.

关 键 词：HAAR小波 算子矩阵 整数阶积分 分数阶积分 Caputo分数阶微分 近似值 平稳信号 非平稳信号 

分 类 号：O175.2[理学—数学]