The Approximate Solutions of 2D- Burger’s Equations
DOI:
https://doi.org/10.32792/jeps.v14i3.454الكلمات المفتاحية:
Burger’s Equations; Atangana-Baleanu fractional operator، fractional variational iteration methodالملخص
This paper investigates the use of the fractional variational iteration method (FVIM) to obtain approximate analytical solutions to two dimensional Burger’s Equations with the Atangana-Baleanu fractional operator (ABFO). This study provides insight on the fractional variational iteration method's accuracy and reliability while approximating fractional differential equation solutions.
المراجع
[ 1] I. Podlubny, FDEs, Mathematics in Science and Engineering, Academic Press, New York (1999).
[ 2] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of FDEs, Vol. 204, Amsterdam, London, and New York, 2006.
[ 3] H. Ahmad, An Analytical Technique to Obtain Approximate Solutions of Nonlinear Fractional PDEs, Journal of Education for Pure Science-University of Thi-Qar, 14(1)(2024) 107-116.
[ 4] M. A. Hussein, Approximate Methods For Solving Fractional Differential Equations, Journal of Education for Pure Science-University of Thi-Qar, 12(2)(2022) 32-40.
[ 5] A. R. Saeid and L. K. Alzaki, Analytical Solutions for the Nonlinear Homogeneous Fractional Biological Equation using a Local Fractional Operator, Journal of Education for Pure Science-
University of Thi-Qar, 13(3), 1-17 (2023).
[ 6] H. Jafari, et al., Local Fractional Adomian Decomposition Method for Solving Two Dimensional Heat conduction Equations within Local Fractional Operators, Journal of Advance in Mathematics, 9 (4)(2014), 2574-2582.
[ 7] H. Jafari, et al., Numerical Solutions of Telegraph and Laplace Equations on Cantor Sets Using Local Fractional Laplace Decomposition Method , International Journal of Advances in Applied Mathematics and Mechanics, 2(3) (2015), 144-151.
[ 8] H. Jafari, et al., A Coupling Method of Local Fractional Variational Iteration Method and Yang-Laplace Transform for Solving Laplace Equation on Cantor Sets, International Journal of pure and Applied Sciences and Technology, 26(1) (2015), 24-33.
[ 9] H. K. Jassim, Local Fractional Laplace Decomposition Method for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow with Local Fractional Derivative, International Journal of Advances in Applied Mathematics and Mechanics, 2(4)(2015), 1-7.
[ 10] H. Ahmad, H. K. Jassim, An Analytical Technique to Obtain Approximate Solutions of Nonlinear Fractional PDEs, Journal of Education for Pure Science-University of Thi-Qar, 14(1)(2024) 107-116.
[ 11] M. A. Hussein, Approximate Methods For Solving Fractional Differential Equations, Journal of Education for Pure Science-University of Thi-Qar, 12(2)(2022) 32-40.
[ 12] A. R. Saeid and L. K. Alzaki, Analytical solutions for the nonlinear homogeneous FBE using a local fractional operator, Journal of Education for Pure Science-University of Thi-Qar, 13(3), 1-17 (2023).
[ 13] H. Jafari, et al., Local Fractional Variational Iteration Method for Nonlinear Partial Differential Equations within Local Fractional Operators, Applications and Applied Mathematics, vol. 10, no. 2, pp. 1055-1065, 2015
[ 14] H. K. Jassim, The Approximate Solutions of Helmholtz and Coupled Helmholtz Equations on Cantor Sets within Local Fractional Operator, Journal of Zankoy Sulaimani-Part A, vol. 17, no. 4, pp. 19-25, 2015.
[ 15] H. Jafari, et al., Approximate Solution for Nonlinear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operator, Journal of Zankoy Sulaimani-Part A, vol. 18, no.1, pp.127-132, 2016
[ 16] H. Jafari, et al., A new approach for solving a system of local fractional partial differential equations, Applications and Applied Mathematics, Vol. 11, No. 1, pp.162-173, 2016.
[ 17] H. Jafari, et al., Application of Local Fractional Variational Iteration Method to Solve System of Coupled Partial Differential Equations Involving Local Fractional Operator, Applied Mathematics & Information Sciences Letters, Vol. 5, No. 2, pp. 1-6, 2017.
[ 18] H. A. Naser, et al., A New Efficient Method for solving Helmholtz and Coupled Helmholtz Equations Involving Local Fractional Operators, 6)4)(2018), 153-157.
[ 19] M. G. Mohammed, et al., The Approximate solutions of time-fractional Burger’s and coupled time-fractional Burger’s equations, International Journal of Advances in Applied Mathematics and Mechanics,6(4)(2019),64-70.
[ 20] M. G. Mohammad, et al., Symmetry Classification of First Integrals for Scalar Linearizable, International Journal of Advances in Applied Mathematics and Mechanics, 7(1) (2019), 20-40.
[ 21] M. Zayir, et al., A Fractional Variational Iteration Approach for Solving Time-Fractional Navier-Stokes Equations. Mathematics and Computational Sciences, 3(2) (2022), 41-47.
[ 22] A. T. Salman, et al., A new approximate analytical method and its convergence for time-fractional differential equations, NeuroQuantology, 20(6) (2022) 3670-3689.
[ 23] M. Y. Zayir, et al,, Solving fractional PDEs by Using FADM within Atangana-Baleanu fractional derivative, AIP Conference Proceedings, 2845(060004) (2023) 1-11.
[ 24] M. Y. Zayir, et al., Approximate Analytical Solutions of Fractional Navier-Stokes Equation, AIP Conference Proceedings, 2834( 080100) (2023) 1-10.
[ 25] S. Kutluay, A. Esen, I. Dag, Numerical solutions of the Burgers’ equations by the least squares quadratic B spline finite element method. J. Comput. Appl. Math. 2004, 167, 21–33.
[ 26] . K. Pandey, L. Verma, A. K. Verma,. On a finite difference scheme for Burgers’ equations. Appl. Math. Comput. 2009, 215, 2206–2214.
[ 27] . E. A. Aksan, A numerical solution of Burgers’ equation by finite element method constructed on the method of discretization in time. Appl. Math. Comput. 2005, 170, 895–904.
[ 28] .M. A. Abdou, A. A.Soliman. Variational iteration method for solving Burgers’ and coupled Burgers’ equations. J. Comput. Appl. Math. 1996, 181, 245–251.
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الحقوق الفكرية (c) 2024 Journal of Education for Pure Science- University of Thi-Qar
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