Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets

被引：12

作者：

Wang, Jiao ^{[1
]}

Xu, Tian-Zhou ^{[1
]}

Wei, Yan-Qiao ^{[2
]}

Xie, Jia-Quan ^{[3
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Univ Orleans, INSA Ctr Val Loire, Bourges, France

[3] Taiyuan Univ Sci & Technol, Coll Mech Engn, Taiyuan, Shanxi, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2019年 / 96卷 / 02期

关键词：

Bernoulli wavelets; fractional integral operator matrix; systems of fractional order differential equations; numerical solutions; convergence analysis; OPERATIONAL MATRIX; COUPLED SYSTEM; ADOMIAN DECOMPOSITION; CONVERGENCE;

D O I：

10.1080/00207160.2018.1438604

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an effective algorithm for solving systems of fractional order differential equations (FDEs) is proposed. The algorithm is based on Bernoulli wavelets function approximation, which has never been used for systems of FDEs. The main purpose of this algorithm is to combine Bernoulli wavelets function approximation with its fractional integral operator matrix to transform the studied systems of fractional differential equations into easily solved systems of algebraic equations. Illustrative examples are included to reveal the effectiveness of the algorithm and the accuracy of the convergence analysis.

引用

页码：317 / 336

页数：20

共 50 条

[21] Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre Wavelets
Yin, Fu-kang
Wu, Jian-ping
Leng, Hong-ze
[J]. 2ND INTERNATIONAL CONFERENCE ON APPLIED MATHEMATICS, SIMULATION AND MODELLING (AMSM 2017), 2017, 162 : 130 - 135
[22] An efficient algorithm based on Gegenbauer wavelets for the solutions of variable-order fractional differential equations
Muhammad Usman
Muhammad Hamid
Rizwan Ul Haq
Wei Wang
[J]. The European Physical Journal Plus, 133
[23] An efficient algorithm based on Gegenbauer wavelets for the solutions of variable-order fractional differential equations
Usman, Muhammad
Hamid, Muhammad
Ul Haq, Rizwan
Wang, Wei
[J]. EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (08):
[24] A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions
Rahimkhani, Parisa
Ordokhani, Yadollah
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (01) : 34 - 59
[25] A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations
P. Rahimkhani
Y. Ordokhani
E. Babolian
[J]. Numerical Algorithms, 2017, 74 : 223 - 245
[26] UNIQUE SOLUTIONS FOR SYSTEMS OF FRACTIONAL ORDER DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
Guo, Zhenyu
Liu, Min
[J]. BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 3 (01): : 142 - 147
[27] A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations
Rahimkhani, P.
Ordokhani, Y.
Babolian, E.
[J]. NUMERICAL ALGORITHMS, 2017, 74 (01) : 223 - 245
[28] Numerical Solutions of Fourth-Order Fractional Integro-Differential Equations
Yildirim, Ahmet
Sezer, Sefa Anil
Kaplan, Yasemin
[J]. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2010, 65 (12): : 1027 - 1032
[29] Numerical solutions of multi-order fractional differential equations by Boubaker Polynomials
Bolandtalat, A.
Babolian, E.
Jafari, H.
[J]. OPEN PHYSICS, 2016, 14 (01): : 226 - 230
[30] An Efficient Method for Numerical Solutions of Distributed-Order Fractional Differential Equations
Jibenja, N.
Yuttanan, B.
Razzaghi, M.
[J]. JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2018, 13 (11):

← 1 2 3 4 5 →