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辽宁工程技术大学学报(自然科学版) 료녕공정기술대학학보(자연과학판)
JOURNAL OF LIAONING TECHNICAL UNIVERSITY NATURAL SCIENCE EDITION
2013年 2期 141-144 ,共4页

彭超%宋向东%仪明旭%魏金侠彭超%宋嚮東%儀明旭%魏金俠

팽초%송향동%의명욱%위금협

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 Haar 小波%算子矩陣%整數階積分%分數階積分%Caputo 分數階微分%近似值%平穩信號%非平穩信號
Haar 소파%산자구진%정수계적분%분수계적분%Caputo 분수계미분%근사치%평은신호%비평은신호
Haar wavelet%operational matrix%integer integral%fractional integrals%Caputo fractional derivatives%approximations%stationary signal%non-stationary signal

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.
계산일류함수분수계적분급기 Caputo 분수계미분적문제.채용 Haar 소파화산자구진상결합적방법,득도일충Haar 소파분수계적분산자구진,이용해산자구진,대급정함수주료유효적리산,충분결합 Haar 소파구진적정교성、희소성,장구분수계미적분문제전화위산자구진적승적,종이편우계산궤구해.평은신호화비평은신호적수치산례험증료해방법적가행성화유효성.
@@@@In this paper, Haar wavelet operational matrix of fractional order integration is given by combining 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.