Efficient Computational Approach for Generalized Fractional KdV–Burgers Equation

被引：0
作者：
Rida S.Z. [1 ]
Hussien H.S. [1 ]
机构：
[1] Mathematics Department, Faculty of Science, South Valley University, Qena
来源：
International Journal of Applied and Computational Mathematics | 2020年 / 6卷 / 6期
关键词：
Collocation method; Error analysis; Fractional calculus; Fractional Korteweg–de Vries and Burgers equations; Mittag–Leffler function;
D O I：
10.1007/s40819-020-00915-1
中图分类号：
学科分类号：
摘要：
A collocation method based on double summations of Mittag–Leffler functions is proposed to solve the Korteweg–de Vries (KdV) and Burgers equation of fractional order with initial-boundary conditions. The resulting algebraic system is constructed as a constrained optimization problem and optimized to obtain the unknown coefficients. Error analysis of the approximation solution is studied. Simulations of the results are studied graphically through representations for the effect of fractional order parameters and time levels. The results ensure that the proposed method is accurate and efficient. © 2020, Springer Nature India Private Limited.
引用
收藏
相关论文
共 50 条
[21]   Shifted Second-Kind Chebyshev Spectral Collocation-Based Technique for Time-Fractional KdV-Burgers' Equation [J].
Atta, Ahmed Gamal ;
Youssri, Youssri Hassan .
IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 2023, 14 (04) :207-224
[22]   Approximation of one and two dimensional nonlinear generalized Benjamin-Bona-Mahony Burgers' equation with local fractional derivative [J].
Ghafoor, Abdul ;
Hussain, Manzoor ;
Ahmad, Danyal ;
Ul Arifeen, Shams .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 172 :125-133
[23]   Soliton Solutions of Fractional Order KdV-Burger's Equation [J].
Younis, Muhammad .
JOURNAL OF ADVANCED PHYSICS, 2014, 3 (04) :325-328
[24]   Some exact solutions for fractional generalized Burgers' fluid in a porous space [J].
Khan, Masood ;
Hayat, Tasawar .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (05) :1952-1965
[25]   Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions [J].
Chen, Li ;
Lu, Shujuan ;
Xu, Tao .
APPLIED NUMERICAL MATHEMATICS, 2021, 169 (169) :164-178
[26]   On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law [J].
Hayat, T. ;
Khan, M. ;
Asghar, S. .
ACTA MECHANICA SINICA, 2007, 23 (03) :257-261
[27]   A Hybrid Scheme for Efficient Numerical Solution of the Fractional Telegraph Equation [J].
El-shenawy, Atallah ;
El-Gamel, Mohamed ;
Teba, Amir .
IRANIAN JOURNAL OF SCIENCE, 2025, 49 (03) :811-824
[28]   On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law [J].
T.Hayat ;
M.Khan ;
S.Asghar .
Acta Mechanica Sinica, 2007, (03) :257-261
[29]   On the MHD flow of fractional generalized Burgers’ fluid with modified Darcy’s law [J].
T. Hayat ;
M. Khan ;
S. Asghar .
Acta Mechanica Sinica, 2007, 23 :257-261
[30]   Homotopy analysis method for space- and time-fractional KdV equation [J].
Mohyud-Din, Syed Tauseef ;
Yildirim, Ahmet ;
Yuluklu, Eda .
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2012, 22 (6-7) :928-941
12345