The Techniques for Solving Fractional Burger's Equations
Khaled Abdalla Ishag *
Department of Basic Sciences, Faculty of Engineering Science, Omdurman Islamic University, Khartoum, Sudan.
Abulfida Mohamed Ahmed
Department of Mathematics, Faculty of Education, University of Nyala, Nyala, Sudan.
Asmaa Eltayeb Ali
Department of Mathematics, Faculty of Science and Technology, Omdurman Islamic University, Khartoum, Sudan.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we applied Homotopy Perturbation Method for solving nonlinear fractional Burger's equations. The fractional derivatives described by Caputo's, the study focus four fractional partial differential equations, by this method the solution considered as the sum of an infinite series, which converges rapidly to exact and compared the fractional order of Burger's differential equations with ordinary order of Burger's differential equations. In addition, the graphical represented the solutions, which had been given by MATLAB program.
Keywords: Palaeorelationship of insects with plants, Fractional calculus, Glossopteris leaves and insects, homotopy perturbation method, burger equation, matlab, caputo derivative
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References
Lokenath Debnath. 'Nonlinear partial differential equations for scientists and engineers. Springer Science and Business; 2005.
Murray R. Spiegel. Theory and problems of fourier analysis with applications to boundary value problems; 1974.
Miller K, Ross B. An introduction to the fractional calculus and fractional differential equations; 1993.
Khaled Abdalla Ishag. A solution of nonlinear model for concrete beams'', Sudan University of Science and Technology; 2019.
Khalid Suliman Aboodh, Abu baker Ahmed. On the application of homotopy analysis method to fractional equation. Journal of the Faculty of Science and Technology. 2020;7:1 -18.
Hossein Ali Eaued, Hassan Kamil Jassim, Mayada Gassab Mohammed. A Novel method for the analytical solution of partial differential equations arising in mathematical physics, 10P Conference Science Materials Science and Engineering; 2020.
Dengguo Xu, Yanmei Li, Weifeng Zhou. Controllability and observability of fractional linear system with two different orders, Hindawi Limited; 2014.
Sangita Choudhary, Varsha Daftardar- Gejji. Solving systems of multi- term fractional partial differential equations, in variant subspace approach, International Journal of Modeling, Simulation, and Scientific Computing; 2019.
Khaled A. Gepreel, Taher A. Nofal, Fowziab M. Alotaibi. Numerical solutions for the time and space fractional nonlinear partial differential equations, Journal of Applied Mathematics; 2013.
Abdulghafor M. Al-Rozbayani, Karam A. Al-Hayalie. Numerical solution of Burger’s_fisher equation in one - dimensional using finite differences methods. Fluid Mechanics. 2018;4(1):20-26.
Joseph M. Kimeu, Fractional calculus: definitions and applications; 2009.
Hunt B, Lipsman R, Rosenberg J, Coombes K, Osborn J, Stuck G. A guide to MATLAB for beginners and experienced users; 2001.
Podlubny I. Fractional differential equations. Academic Press, San Diego, California, USA; 1998.
Christina Kuttler, Reaction – diffusion equations with applications; 2011.
Mainardi F, Luchko Y, Pagnini G. The fundamental solution of the space time fractional diffusion equation. Fractional Calculus and Applied Analysis. 2001;4:153 -192.