Title: Homotopy Perturbation Method for Solving the Fractional Fisher's Equation
Author(s): Mountassir Hamdi Cherif, Kacem Belghaba, Djelloul Ziane
Pages: 9-16
Cite as:
Mountassir Hamdi Cherif, Kacem Belghaba, Djelloul Ziane, Homotopy Perturbation Method for Solving the Fractional Fisher's Equation, Int. J. Anal. Appl., 10 (1) (2016), 9-16.


In this paper, we apply the modified HPM suggested by Momani and al. [23] for solving the time-fractional Fisher's equation and we use the classical HPM to derive numerical solutions of the space-fractional Fisher's equation. We compared our solution with the exact solution. The results show that the HPM modified is an appropriate method for solving nonlinear fractional derivative equations.

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  1. A. Hanyga, Fractional-order relaxation laws in non-linear viscoelasticity, Continuum Mechanics and Thermodynamics, 19 (2007), 25-36.

  2. V. E. Tarasov, Fractional integro-differential equations for electromagnetic waves in dielectric media, Theoretical and Math. Phys, 158 (2009), 355-359.

  3. G. Chen and G. Friedman, An RLC interconnect model based on Fourier analysis, Comput. Aided Des. Integr. Circuits Syst, 24 (2005), 170-183.

  4. T. J. Anastasio, The fractional-order dynamics of brainstem vestibule-oculumotor neurons, Biol. Cybern, 72 (1994), 69-79.

  5. J. H. He, Homotopy perturbation technique, Comput. Meth. Appl. Mech. Eng, 178 (1999), 257-262.

  6. J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), 695-700.

  7. J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. of Nonlinear Mech, 35 (2000), 37-43.

  8. J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Modern Phys, B 20 (2006), 1141-1199.

  9. J. H. He, A new perturbation technique which is also valid for large parameters, J. Sound Vib, 229 (2000), 1257-1263.

  10. A. J. Khaleel, Homotopy perturbation method for solving special types of nonlinear Fredholm integro-differentiel equations, J. Al-Nahrain Uni, 13 (2010), 219-224.

  11. D. D. Ganji, H. Babazadeh, F. Noori, M. M. Pirouz and M. Janipour, An Application of Homotopy Perturbation Method for Non-linear Blasius Equation to Boundary Layer Flow Over a Flat Plate, Int. J. Nonlinear Sci, 7 (2009), 399-404.

  12. R. Taghipour, Application of homotopy perturbation method on some linear and nonlnear parabolique equations, IJRRAS, 6 (2011), 55-59.

  13. W. Asghar Khan, Homotopy Perturbation Techniques for the Solution of Certain Nonlinear Equations, Appl. Math. Sci, 6 (2012), 6487-6499.

  14. S. M. Mirzaei, Homotopy Perturbation Method for Solving the Second Kind of Non-Linear Integral Equations, Int. Math. Forum, 5 (2010), 1149-1154.

  15. H. El Qarnia, Application of homotopy perturbation method to non-homogeneous parabolic partial and non linear differential equations, W. J. Mod. Simul, 5 (2009), 225-231.

  16. A. J. Al-Saif and D. A. Abood, The Homotopy Perturbation Method for Solving K(2,2) Equation, J. Basrah Researches ((Sciences)), 37 (2011).

  17. M. Matinfar, M. Mahdavi and Z. Raeisy, The implementation of Variational Homotopy Perturbation Method for Fisher’s equation, Int. J. of Nonlinear Sci, 9 (2010), 188-194.

  18. I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.

  19. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

  20. K. Diethelm, The Analysis Fractional Differential Equations, Springer-Verlag Berlin Heidelberg, 2010.

  21. J. Biazar and H. Ghazvini, Convergence of the homotopy perturbation method for partial dfferential equations, Nonlinear Analysis: Real World Applications, 10 (2009), 2633-2640.

  22. J. Biazar and H. Aminikhah, Study of convergence of homotopy perturbation method for systems of partial differential equations, Comput. Math. Appli, 58 (2009), 2221-2230.

  23. S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A 365 (2007), 345-350.

  24. M. Matinfar, Z. Raeisi and M. Mahdavi, Variational Homotopy Perturbation Method for the Fisher’s Equation, Int. J. of Nonlinear Sci, 9 (2010), 374-378.

  25. A. Bouhassoun and M. Hamdi Cherif, Homotopy Perturbation Method For Solving The Fractional Cahn-Hilliard Equation, Journal of Interdisciplinary Mathematics, 18 (2015), 513-524.