The Legendre wavelet method for solving fractional differential equations

被引：192

作者：

Rehman, Mujeeb Ur ^{[1
]}

Khan, Rahmat Ali ^{[2
]}

机构：

[1] NUST, Ctr Adv Math & Phys, Sector H 12, Islamabad, Pakistan

[2] Univ Malakand, Chakdara Dir L, Khyber Pakhutoo, Pakistan

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 11期

关键词：

Fractional differential equations; Operational matrices; Legendre wavelets; BOUNDARY-VALUE PROBLEM; NUMERICAL-SOLUTION; OPERATIONAL MATRIX; INTEGRAL-EQUATIONS;

D O I：

10.1016/j.cnsns.2011.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional differential equations are solved using the Legendre wavelets. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. The illustrative examples are provided to demonstrate the applicability, simplicity of the numerical scheme based on the Legendre. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：4163 / 4173

页数：11

共 33 条

[1] Dynamics of the fractional oscillator
Achar, BNN
Hanneken, JW
Enck, T
Clarke, T
[J]. PHYSICA A, 2001, 297 (3-4): : 361 - 367
[2] [Anonymous], 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0
[3] [Anonymous], 2000, Applications of Fractional Calculus in Physics
[4] [Anonymous], 1999, FRACTIONAL DIFFERENT
[5] [Anonymous], SIAM J MATH ANAL, DOI DOI 10.1137/S0036141095295127
[6] Solution of fractional differential equations by using differential transform method
Arikoglu, Aytac
Ozkol, Ibrahim
[J]. CHAOS SOLITONS & FRACTALS, 2007, 34 (05) : 1473 - 1481
[7] Positive solutions for boundary value problem of nonlinear fractional differential equation
Bai, ZB
Lü, HS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) : 495 - 505
[8] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2
CAPUTO, M
[J]. GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05): : 529 - &
[9] Haar wavelet method for solving lumped and distributed-parameter systems
Chen, CF
Hsiao, CH
[J]. IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS, 1997, 144 (01): : 87 - 94
[10] Diethelm K, 2002, BIT, V42, P490

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