Numerical solution of fractional differential equations using fractional Chebyshev polynomials

被引：2
|
作者：
Ozturk, Yalcin [1 ]
Unal, Mutlu [2 ]
机构：
[1] Mugla Sitki Kocman Univ, Ula Ali Koman Vocat Sch, Mugla, Turkey
[2] Mugla Sitki Kocman Univ, Fac Sci, Dept Math, Mugla, Turkey
来源：
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 03期
关键词：
Bagley-Torvik equation; fractional relaxation-oscillation equation; fractional differential equation; Factional order Chebyshev polynomials; approximate solution; collocation method; BOUNDARY-VALUE-PROBLEMS; APPROXIMATE SOLUTION; OPERATIONAL MATRIX;
D O I：
10.1142/S1793557122500486
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, fractional order Chebyshev polynomials are presented and some properties are given. Using definition of fractional order Chebyshev polynomials, we give a numerical scheme for solving fractional differential equation by the collocation method. The Collocation method converts the given fractional differential equation into a matrix equation, which yields a linear algebraic system. Bagley-Torvik equation and fractional relaxation-oscillation equation are solved to show the effectiveness of the given method. This method is compared with some known schemes.
引用
收藏
页数：21
相关论文
共 50 条
  • [1] A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations
    Darani, Mohammadreza Ahmadi
    Nasiri, Mitra
    [J]. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2013, 1 (02): : 96 - 107
  • [2] Chebyshev polynomials for approximation of solution of fractional partial differential equations with variable coefficients
    Yang Zhongshu
    Zhang Hongbo
    [J]. PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATERIAL, MECHANICAL AND MANUFACTURING ENGINEERING, 2015, 27 : 252 - 260
  • [3] Solution of Fractional Differential Equations by Using Conformable Fractional Differential Transform Method with Adomian Polynomials
    Teppawar, R. S.
    Ingle, R. N.
    Muneshwar, R. A.
    [J]. MATHEMATICS AND COMPUTING, ICMC 2022, 2022, 415 : 349 - 362
  • [4] Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials
    Nemati, Somayeh
    Lima, Pedro M.
    Torres, Delfim F. M.
    [J]. FRACTAL AND FRACTIONAL, 2021, 5 (04)
  • [5] Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations
    Arman Dabiri
    Eric A. Butcher
    [J]. Nonlinear Dynamics, 2017, 90 : 185 - 201
  • [6] The fractional Chebyshev collocation method for the numerical solution of fractional differential equations with Riemann-Liouville derivatives
    Dabiri, Arman
    Karimi, Laya
    [J]. 2019 AMERICAN CONTROL CONFERENCE (ACC), 2019, : 5493 - 5498
  • [7] Chebyshev polynomials for higher order differential equations and fractional powers
    Bezerra, Flank D. M.
    Santos, Lucas A.
    [J]. MATHEMATISCHE ANNALEN, 2024, 388 (01) : 675 - 702
  • [8] Chebyshev polynomials for higher order differential equations and fractional powers
    Flank D. M. Bezerra
    Lucas A. Santos
    [J]. Mathematische Annalen, 2024, 388 : 675 - 702
  • [9] Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations
    Dabiri, Arman
    Butcher, Eric A.
    [J]. NONLINEAR DYNAMICS, 2017, 90 (01) : 185 - 201
  • [10] Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets
    Chen, Yiming
    Sun, Lu
    Li, Xuan
    Fu, Xiaohong
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2013, 90 (05): : 359 - 378
12345