The Techniques for Solving Nonlinear Fractional Reduction-Diffusion Equations
DOI:
https://doi.org/10.52981/jfst.vi8.1968Keywords:
Fractional calculus, Adomian's decomposition method, Diffusion equationsAbstract
In this paper, Adomian's Decomposition Method (ADM), was applied to solving nonlinear fractional redaction-diffusion equations. Caputo’s describes the fractional derivatives. Study four fractional partial differential equations, heat equation, Burger's equation, Fisher's equation and Burgers-Fisher equation. By this method, the solution considered as the sum of an infinite series. In addition, our graphical represented of the solutions have been given by using MATLAB program.
References
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Podlubny.I.. Fractional Differential Equations. Academic Press, San Diego, California, USA, 1998.
Christina Kuttler, Reaction – diffusion Equations with Applications, 2011.
Hundsdorfer.W. and J. Verwer. Numerical Solution of Time Dependent Advection Diffusion Reaction Equations, Springer, 2003
Hunt. B., R. Lipsman, J. Rosenberg, K. Coombes, J. Osborn, G. Stuck; A Guide to MATLAB for Beginners and Experienced Users, , 2001
Igor Podlubny, Fractional Differential Equations, 1999.
Joseph M. Kimeu, Fractional Calculus: Definitions and Applications, 2009.
Khaled Abdalla, A Solution of Nonlinear Model for Concrete Beams, Sudan University of Science and Technology, 2019.
Khalid Suliman Aboodh and Abu baker Ahmed; On the Application of Homotopy Analysis Method to Fractional Equation, Journal of the Faculty of Science and Technology, 7(2020) 1 -18.
Lokenath Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Fourth Edition, 2007.
Mainardi.F., Y. Luchko and G. pagnini; The Fundamental Solution of The Space Time fractional Diffusion Equation, Fractional calculus and Applied Analysis 4(2001) 153 -192.
Miller K, B. Ross; an Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, Inc., 1993.
Murray R. Spiegel, Theory and Problems of Fourier analysis with Applications to Boundary Value Problems, 1973.
Podlubny.I.. Fractional Differential Equations. Academic Press, San Diego, California, USA, 1998.
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Published
2022-02-08
How to Cite
Khaled Abdalla Ishag. (2022). The Techniques for Solving Nonlinear Fractional Reduction-Diffusion Equations. Journal of The Faculty of Science and Technology, (8), 121–140. https://doi.org/10.52981/jfst.vi8.1968
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