Modified wavelets-based algorithm for nonlinear delay differential equations of fractional order

被引:20
|
作者
Iqbal, Muhammad Asad [2 ]
Shakeel, Muhammad [2 ]
Mohyud-Din, Syed Tauseef [1 ]
Rafiq, Muhammad [3 ]
机构
[1] HITEC Univ, Dept Math, Fac Sci, Taxila, Pakistan
[2] Mohi Ud Din Islamic Univ, Dept Math, Nerian Sharif Ajk, Pakistan
[3] COMSATS Inst Informat Technol, Dept Math, Wah Cantt, Pakistan
来源
ADVANCES IN MECHANICAL ENGINEERING | 2017年 / 9卷 / 04期
关键词
Gegenbauer wavelet method; method of steps; delay differential equations; fractional differential equations; exact solution; BOUNDARY-VALUE-PROBLEMS; INTEGRAL-EQUATIONS; NUMERICAL-SOLUTION; DIFFUSION;
D O I
10.1177/1687814017696223
中图分类号
O414.1 [热力学];
学科分类号
摘要
Most of the physical phenomena located around us are nonlinear in nature and their solutions are of great significance for scientists and engineers. In order to have a better representation of these physical phenomena, fractional calculus is developed. Some of these nonlinear physical models can be represented in the form of delay differential equations of fractional order. In this article, a new method named Gegenbauer Wavelets Steps Method is proposed using Gegenbauer polynomials and method of steps for solving nonlinear fractional delay differential equations. Method of steps is used to convert the fractional nonlinear fractional delay differential equation into a fractional nonlinear differential equation and then Gegenbauer wavelet method is applied at each iteration of fractional differential equation to find the solution. To check the accuracy and efficiency of the proposed method, the proposed method is implemented on different nonlinear fractional delay differential equations including singular-type problems also.
引用
收藏
页码:1 / 8
页数:8
相关论文
共 50 条
  • [41] Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion
    Heydari, M. H.
    Avazzadeh, Z.
    Mahmoudi, M. R.
    CHAOS SOLITONS & FRACTALS, 2019, 124 : 105 - 124
  • [43] Implicit nonlinear fractional differential equations of variable order
    Benkerrouche, Amar
    Souid, Mohammed Said
    Sitthithakerngkiet, Kanokwan
    Hakem, Ali
    BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)
  • [44] Implicit nonlinear fractional differential equations of variable order
    Amar Benkerrouche
    Mohammed Said Souid
    Kanokwan Sitthithakerngkiet
    Ali Hakem
    Boundary Value Problems, 2021
  • [45] NONLINEAR IMPLICIT DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER AT RESONANCE
    Benchohra, Mouffak
    Bouriah, Soufyane
    Graef, John R.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
  • [46] The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers' Equations with Time-Fractional Derivative
    Ozdemir, Neslihan
    Secer, Aydin
    Bayram, Mustafa
    MATHEMATICS, 2019, 7 (06)
  • [47] Oscillation for higher order nonlinear delay differential equations
    Wang, XP
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 157 (01) : 287 - 294
  • [48] Nonlinear oscillation of first order delay differential equations
    Yoshida, N
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1996, 26 (01) : 361 - 373
  • [49] An Extended Predictor-Corrector Algorithm for Variable-Order Fractional Delay Differential Equations
    Moghaddam, B. Parsa
    Yaghoobi, Sh.
    Tenreiro Machado, J. A.
    JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2016, 11 (06):
  • [50] Error analysis of a Haar wavelets-based numerical method with its application to a nonlinear fractional dengue model
    Prakash, Bijil
    Setia, Amit
    Bose, Shourya
    Agarwal, Ravi P. P.
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2024, 101 (12) : 1379 - 1397