Homotopy Analysis Method for Fractional Reaction-Diffusion Equation with Ecological Parameters
Keywords:
Homotopy analysis method, fractional calculus, reaction-diffusion equationAbstract
This paper applies the Homotopy Analysis Method (HAM) to obtain analytical solutions of fractional reaction-diffusion equations with ecological parameters, which arise very frequently in mechanical engineering, control theory, solid mechanics and applied sciences. Numerical results reveal the complete compatibility of proposed algorithm for such problems. Some examples are presented to show the efficiency and simplicity of the method.
doi:10.14456/WJST.2014.37
Downloads
Metrics
References
S Abbasbandy. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem. Eng. J. 2008; 136, 144-50.
S Abbasbandy. Homotopy analysis method for heat radiation equations. Int. Comm. Heat Mass Tran. 2007; 34, 380-7.
S Abbasbandy. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys. Lett. A 2007; 361, 478-83.
T Hayat, M Khan and S Asghar. Homotopy analysis of MHD flows of an Oldroyd 8- constant fluid. Acta Mech. 2004; 168, 213-32.
T Hayat, M Khan and S Asghar. Magneto hydrodynamic flow of an Oldroyd 6-constant fluid. Appl. Math. Comput. 2004; 155, 417-25.
SJ Liao. An approximate solution technique which does not depend upon small parameters (II): An application in fluid mechanics. Int. J. Nonlinear Mech. 1997, 32, 815-22.
SJ Liao. An explicit, totally analytic approximation of Blasius viscous flow problems. Int .J. Nonlinear Mech. 1999; 34, 759-78.
SJ Liao. On the analytic solution of magneto hydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 2003; 488, 189-212.
SJ Liao. An analytic approximate approach for free oscillations of self-excited systems. Int. J. Nonlinear Mech. 2004; 39, 271-80.
SJ Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004; 147, 499-513.
ST Mohyud-Din and MA Noor. Variational iteration method for solving higher-order nonlinear boundary value problems using He’s polynomials. Int. J. Nonlinear Sci. Numer. Simulat. 2008; 9, 141-57.
I Podlubny. Fractional Differential Equations, An Introduction to Fractional Derivatives Fractional Differential Equations, some Methods of Their Solution and some of Their Applications. 1st ed. Academic Press, San Diego, 1999, p. 1-340.
M Caputo. Linear models of dissipation whose Q is almost frequency independent, Part II. J. Roy. Astr. Soc.1967; 13, 529-35.
YA Rossikhin and MV Shitikova. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 1997; 50, 15-67.
A Yildirim and ST Mohyud-Din. Analytical approach to space and time fractional Burger’s equations. Chin. Phys. Lett. 2010; 27, 090501.
A Yildirim and ST Mohyud-Din. The numerical solution of the three-dimensional Helmholtz equations. Chin. Phys. Lett. 2010; 27, 060201.
S Momani. An algorithm for solving the fractional convection-diffusion equation with nonlinear source term. Commun. Nonlinear. Sci. Numer. Simulat. 2007; 12, 1283-90.
Z Odibat and S Momani. Numerical solution of Fokker-Planck equation with space and time-fractional derivatives. Phys. Lett. A 2007; 369, 349-58.
JD Murray. Mathematical Biology. 2nd ed. Springer-Verlag, Berlin, 1993, p. 1-554.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2013 Walailak University
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.