Numerical solution of fractional differential equations using the generalized block pulse operational matrix

被引：158

作者：

Li, Yuanlu ^{[1
]}

Sun, Ning ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Coll Informat & Control, Nanjing 210044, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Operational matrix; Fractional calculus; Fractional differential equations; HOMOTOPY ANALYSIS METHOD; LINEAR-SYSTEMS; PARAMETER-IDENTIFICATION; LEGENDRE POLYNOMIALS; INTEGRAL-EQUATIONS; FOURIER-SERIES; 2ND KIND; ORDER; CALCULUS; CONTROLLERS;

D O I：

10.1016/j.camwa.2011.03.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Riemann-Liouville fractional integral for repeated fractional integration is expanded in block pulse functions to yield the block pulse operational matrices for the fractional order integration. Also, the generalized block pulse operational matrices of differentiation are derived. Based on the above results we propose a way to solve the fractional differential equations. The method is computationally attractive and applications are demonstrated through illustrative examples. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.

引用

页码：1046 / 1054

页数：9

共 38 条

[1]

[Anonymous], INT J INTELLIGENT CO

[2] Solution of fractional differential equations by using differential transform method [J].

Arikoglu, Aytac ;

Ozkol, Ibrahim .

CHAOS SOLITONS & FRACTALS, 2007, 34 (05) :1473-1481

[3] Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions [J].

Babolian, E. ;

Masouri, Z. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) :51-57

[4] Fractional order control strategies for power electronic buck converters [J].

Calderon, A. J. ;

Vinagre, B. M. ;

Feliu, V. .

SIGNAL PROCESSING, 2006, 86 (10) :2803-2819

[5] WALSH OPERATIONAL MATRICES FOR FRACTIONAL CALCULUS AND THEIR APPLICATION TO DISTRIBUTED SYSTEMS [J].

CHEN, CF ;

TSAY, YT ;

WU, TT .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1977, 303 (03) :267-284

[6] STATE-SPACE APPROACH TO WALSH SERIES SOLUTION OF LINEAR-SYSTEMS [J].

CHEN, CF ;

HSIAO, CH .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1975, 6 (09) :833-858

[7]

Chyi H., 1982, CHEM ENG J, V25, P39

[8] Analytical solution of a fractional diffusion equation by variational iteration method [J].

Das, S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 57 (03) :483-487

[9] A new set of orthogonal functions and its application to the analysis of dynamic systems [J].

Deb, A ;

Dasgupta, A ;

Sarkar, G .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2006, 343 (01) :1-26

[10] BLOCK-PULSE FUNCTIONS, THE MOST FUNDAMENTAL OF ALL PIECEWISE-CONSTANT BASIS FUNCTIONS [J].

DEB, A ;

SARKAR, G ;

SEN, SK .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1994, 25 (02) :351-363

← 1 2 3 4 →