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Chunfu Wei

SOLVING TIME-SPACE FRACTIONAL FITZHUGH-NAGUMO EQUATION BY USING HE-LAPLACE DECOMPOSITION METHOD

ABSTRACT
This paper proposes a new method to solve fractional differential equations, which takes full advantages of He's homotopy perturbation, Laplace transform, and He's polynomials and it is named as He-Laplace decomposition method. The time-space fractional Fitzhugh-Nagumo equation is used as example to elucidate the solution process, and the obtained results are of high accuracy. The new method sheds a new light on analytical approach to fractional calculus.
KEYWORDS
time-space fractional Fitzhugh-Nagumo equation, He-Laplace decomposition method, Caputo derivative
PAPER SUBMITTED: 2017-01-22
PAPER REVISED: 2017-09-27
PAPER ACCEPTED: 2017-09-27
PUBLISHED ONLINE: 2018-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI1804723W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1723 - 1728]
REFERENCES
  1. Diethelm, Kai, Neville J. Ford, Analysis of Fractional Differential Equations, Journal of Mathematical Analysis and Applications, 265 (2002), 2, pp. 229-248
  2. Heymans, N., Podlubny, I., Physical Interpretation of Initial Conditions for Fractional Differential Equa-tions with Riemann-Liouville Fractional Derivatives, Rheologica Acta, 45 (2006), 5, pp. 765-771
  3. Povstenko, Yu. Z., Fractional Heat Conduction Equation and Associated Thermal Stress, Journal of Thermal Stresses, 28 (2004), 1, pp. 83-102
  4. Yang, X.-J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differen-tial Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67 (2015), 3, pp. 752-761
  5. He, J.-H., et al., Geometrical Explanation of the Fractional Complex Transform and Derivative Chain Rule for Fractional Calculus, Physics Letters A, 376 (2012), 4, pp. 257-259
  6. Wazwaz, A. M., Gorguis, A., Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients, Applied Mathematics and Computation, 149 (2004), 1, pp. 15-29
  7. Povstenko, Y. Z, Thermoelasticity that Uses Fractional Heat Conduction Equation, Journal of Mathe-matical Sciences, 162 (2009), 2, pp. 296-305
  8. Kenyon, R., Okounkov, A., Limit Shapes and the Complex Burgers Equation, Acta Mathematica, 199 (2007), 2, pp. 263-302
  9. Oldham, K. B, Fractional Differential Equations in Electrochemistry, Advances in Engineering Software, 41 (2010), 1, pp. 9-12
  10. Agrawal, O. P., Application of Fractional Derivatives in Thermal Analysis of Disk Brakes, Nonlinear Dynamics, 38 (2004), 1, pp. 191-206
  11. Ezzat, M. A., El-Karamany, A. S., Fractional Order Theory of a Perfect Conducting Thermoelastic Me-dium, Canadian Journal of Physics, 89 (2011), 3, pp. 311-318
  12. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  13. Dehghan, M., et al., Application of Semi Analytic Methods for the Fitzhugh-Nagumo Equation, which Models the Transmission of Nerve Impulses, Mathematical Methods in the Applied Sciences, 33 (2010), 11, pp. 1384-1398
  14. Elmer, C. E., Van Vleck, E. S., Spatially Discrete FitzHugh-Nagumo Equations, SIAM Journal on Ap-plied Mathematics, 65 (2005), 4, pp. 1153-1174
  15. Abbasbandy, S., Soliton Solutions for the Fitzhugh-Nagumo Equation with the Homotopy Analysis Method, Applied Mathematical Modelling, 32 (2008), 12, pp. 2706-2714
  16. Alford, J. G., Auchmuty, G., Rotating Wave Solutions of the FitzHugh-Nagumo Equations, Journal of Mathematical Biology, 53 (2006), 5, pp. 797-819
  17. Guckenheimer, J., Kuehn, C., Homoclinic Orbits of the FitzHugh-Nagumo Equation:Bifurcations in the Full System, SIAM Journal on Applied Dynamical Systems, 9 (2010), 1, pp. 138-153
  18. Rida, S. Z., et al., On the Solutions of Time-Fractional Reaction-Diffusion Equations, Communications in Nonlinear Science and Numerical Simulation, 15 (2010), 12, pp. 3847-3854
  19. Hariharan, G., Rajaraman, R., Two Reliable Wavelet Methods to Fitzhugh-Nagumo (FN) and Fractional FN Equations, Journal of Mathematical Chemistry, 51 (2013), 9, pp. 2432-2454
  20. Mohyud-Din, S. T., et al., Travelling Wave Solutions of Seventh-Order Generalized KdV Equations Us-ing He's Polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 2, pp. 223-229
  21. Widder, D. V., Laplace Transform (PMS-6). Princeton University Press, Princeton, N. J., USA, 2015
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Solving time-space fractional Fitzhugh-Nagumo equation by using He-Laplace decomposition method

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