Legendre wavelets approach for numerical solutions of distributed order fractional differential equations

被引：87
|
作者：
Yuttanan, Boonrod [1 ]
Razzaghi, Mohsen [2 ]
机构：
[1] Prince Songkla Univ, Fac Sci, Dept Math & Stat, Algebra & Applicat Res Unit, Hat Yai 90112, Thailand
[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA
来源：
APPLIED MATHEMATICAL MODELLING | 2019年 / 70卷
关键词：
Legendre wavelets; Distributed order; Fractional differential equations; Caputo derivative; OPERATIONAL MATRIX; DELAY SYSTEMS; BLOCK-PULSE; INTEGRODIFFERENTIAL EQUATIONS; HYBRID; INTEGRATION; CALCULUS; MODEL;
D O I：
10.1016/j.apm.2019.01.013
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this study, a new numerical method for the solution of the linear and nonlinear distributed fractional differential equations is introduced. The fractional derivative is described in the Caputo sense. The suggested framework is based upon Legendre wavelets approximations. For the first time, an exact formula for the Riemann-Liouville fractional integral operator for the Legendre wavelets is derived. We then use this formula and the properties of Legendre wavelets to reduce the given problem into a system of algebraic equations. Several illustrative examples are included to observe the validity, effectiveness and accuracy of the present numerical method. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：350 / 364
页数：15
相关论文
共 50 条
  • [1] Numerical solutions of distributed order fractional differential equations in the time domain using the Muntz-Legendre wavelets approach
    Maleknejad, Khosrow
    Rashidinia, Jalil
    Eftekhari, Tahereh
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (01) : 707 - 731
  • [2] Numerical solutions of fractional partial differential equations by using Legendre wavelets
    Yi, Mingxu (yimingxu88@163.com), 2016, International Association of Engineers (24)
  • [3] Numerical Solutions of Fractional Partial Differential Equations by Using Legendre Wavelets
    Song, Hao
    Yi, Mingxu
    Huang, Jun
    Pan, Yalin
    ENGINEERING LETTERS, 2016, 24 (03) : 358 - 364
  • [4] Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets
    Chen, Yi-Ming
    Wei, Yan-Qiao
    Liu, Da-Yan
    Yu, Hao
    APPLIED MATHEMATICS LETTERS, 2015, 46 : 83 - 88
  • [5] Numerical solutions for systems of fractional order differential equations with Bernoulli wavelets
    Wang, Jiao
    Xu, Tian-Zhou
    Wei, Yan-Qiao
    Xie, Jia-Quan
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2019, 96 (02) : 317 - 336
  • [6] 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
    2ND INTERNATIONAL CONFERENCE ON APPLIED MATHEMATICS, SIMULATION AND MODELLING (AMSM 2017), 2017, 162 : 130 - 135
  • [7] Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
    Yuttanan, Boonrod
    Razzaghi, Mohsen
    Vo, Thieu N.
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2023, 24 (01) : 57 - 69
  • [8] Numerical solutions for distributed-order fractional optimal control problems by using Muntz-Legendre wavelets
    Razzaghi, Mohsen
    Vo, Thieu N.
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2022, 478 (2258):
  • [9] Application of Legendre wavelets for solving fractional differential equations
    Jafari, H.
    Yousefi, S. A.
    Firoozjaee, M. A.
    Momani, S.
    Khalique, C. M.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1038 - 1045
  • [10] Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials
    Shah, Kamal
    Naz, Hafsa
    Abdeljawad, Thabet
    Khan, Aziz
    Alqudah, Manar A.
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2023, 134 (02): : 941 - 955
12345