A Numerical Method for Delayed Fractional-Order Differential Equations

被引：121

作者：

Wang, Zhen ^{[1
,2
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Informat Sci & Engn, Qingdao 266590, Peoples R China

[2] Nanjing Univ, State Key Lab Novel Software Technol, Nanjing 210093, Jiangsu, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS | 2013年

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

PREDICTOR-CORRECTOR APPROACH; SYSTEM; DERIVATIVES; CHAOS;

D O I：

10.1155/2013/256071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method.

引用

页数：7

共 50 条

[41] A novel high-order algorithm for the numerical estimation of fractional differential equations [J].

Asl, Mohammad Shahbazi ;

Javidi, Mohammad ;

Yan, Yubin .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 342 :180-201

[42] Fundamental solutions of the general fractional-order diffusion equations [J].

Yang, Xiao-Jun ;

Gao, Feng ;

Ju, Yang ;

Zhou, Hong-Wei .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (18) :9312-9320

[43] On the concept of general solution for impulsive differential equations of fractional-order q ∈ (2,3) [J].

Zhang, Xianmin ;

Shu, Tong ;

Liu, Zuohua ;

Ding, Wenbin ;

Peng, Hui ;

He, Jun .

OPEN MATHEMATICS, 2016, 14 :452-473

[44] On the Solution of the Fractional-Order Pneumonia Model Using Numerical Computational Methods [J].

Alalyani, Ahmad .

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, 17 (04) :2763-2799

[45] Synchronization of Fractional-Order Delayed Neural Networks with Hybrid Coupling [J].

Bao, Haibo ;

Park, Ju H. ;

Cao, Jinde .

COMPLEXITY, 2016, 21 (S1) :106-112

[46] State estimation of fractional-order delayed memristive neural networks [J].

Bao, Haibo ;

Cao, Jinde ;

Kurths, Juergen .

NONLINEAR DYNAMICS, 2018, 94 (02) :1215-1225

[47] Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials [J].

Usman, M. ;

Hamid, M. ;

Zubair, T. ;

Haq, R. U. ;

Wang, W. ;

Liu, M. B. .

APPLIED MATHEMATICS AND COMPUTATION, 2020, 372

[48] CHAOTIC VIBRATION OF NONLINEAR FRACTIONAL-ORDER DIFFERENTIAL OSCILLATOR [J].

Zhang, W. ;

Huang, F. ;

Li, B. H. ;

Li, G. ;

Zheng, L. M. ;

Wang, X. L. .

ENVIRONMENTAL VIBRATIONS: PREDICTION, MONITORING, MITIGATION AND EVALUATION, VOLS I AND II, 2009, :937-941

[49] Dynamic behaviors of nonlinear fractional-order differential oscillator [J].

Wei Zhang ;

Shao-kai Liao ;

Nobuyuki Shimizu .

Journal of Mechanical Science and Technology, 2009, 23 :1058-1064

[50] Dynamic behaviors of nonlinear fractional-order differential oscillator [J].

Zhang, Wei ;

Liao, Shao-kai ;

Shimizu, Nobuyuki .

JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY, 2009, 23 (04) :1058-1064

← 1 2 3 4 5 →