HE’S FRACTIONAL DERIVATIVE AND ITS APPLICATION FOR FRACTIONAL FORNBERG-WHITHAM EQUATION

Main Article Content

San-Yang LIU Kang-Le WANG

Abstract

Fractional Fornberg-Whitham equation with He’s fractional derivative is studied in a fractal process. The fractional complex transform is adopted to convert the studied fractional equation into a differential equation, and He's homotopy perturbation method (HPM) is used to solve the equation.

Article Details

How to Cite
LIU, San-Yang; WANG, Kang-Le. HE’S FRACTIONAL DERIVATIVE AND ITS APPLICATION FOR FRACTIONAL FORNBERG-WHITHAM EQUATION. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2225>. Date accessed: 14 dec. 2017. doi: https://doi.org/10.2298/TSCI151025054W.
Section
Articles
Received 2017-03-06
Accepted 2017-03-13
Published 2017-03-13

References

[1] He, J.H., et al., A new fractional derivative and its application to explanation of polar bear hairs, Journal of King Saud University Science, 2015.
[2] He, J.H., A tutorial review on fractal spacetime and fractional calculus, Int. J. Theor. Phys. 53(2014), 11, pp.3698-3718 .
[3] He, J.H., A new fractal derivation. Therm. Sci. 15(2011), pp. 145-147.
[4] Podlubny, I., Fractional Differential Equations, Academic, New York, 1999.
[5] Yang, X. J., Advanced Local Fractional Calculus and Its Applications. World Science Publisher, New York, USA, 2012.
[6] He, J.H., A short remark on fractional variational iteration method, Phys. Lett. A 375(2011), pp. 3362-3364.
[7] Yang,A.M., et al.,Laplace variational iteration for the two-dimensional diffusion equation in homogeneous materials, Therm. Sci. 19(2015), pp. 163-168.
[8] Lin, J., Lu.J. F., Variational iteration method for the classical drinfel'D-Sokolov-Wilson equation,Therm.Sci.18(2014),5,pp. 1543-1546.
[9] He, J.H., Variational iteration method-Some recent results and new interpretations,J. Comput. Appl. Math. 207(2007), pp. 3-17.
[10] Lu, J. F., An analytical approach to the Fornberg-Whitham equation type equations by using the variational iteration method. Comput. Math. Applicat. 61(2011), pp. 2010-2013.
[11] Huang, L. L., Matrix Lagrange multiplier of the VIM, Journal of Computational Complexity and Applications, 2 (2016), 3, pp. 86-88
[12] Liu, J. F., Modified variational iteration method for varian Boussinesq equation, Therm.Sci., 19(2015), 4, pp.1195-1199
[13] He, J.H., Exp-function Method for Fractional Differential Equations, Int. J. Nonlinear Sci.Numer. 6(2013), pp. 363-366.
[14] Jia,S.,M.et al., Exact solution of fractional Nizhnik-Novikov-Veselov equation, Therm. Sci. 18(2014), 5, pp. 1716-1717.
[15] Ma, H.C., et al., Exact solutions of nonlinear fractional partial differential equations by fractional sub-equation method, Therm. Sci,19(2015), 4, pp. 1239-1244 .
[16] He, J.H., Homotopy perturbation technique,Computer Methods in Applied Mechanics and Engineering. 178(1999), pp. 257-262.
[17] He, J.H., A coupling method of a homotopy technique and a perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics. 35(2000), pp. 37-43.
[18] He, J.H., Application of homotopy perturbation method to nonlinear wave equation, Chaos, Solitons and Fractals, 26(2005), pp. 695-700.
[19] Rajeev., Homotopy perturbation method for a Stefan problem with variable latent heat, Therm. Sci. 18(2014), 2, pp. 391-398.
[20] Zhang,M.F., et al., Efficient homotopy perturbation method for fractional nonlinear equations using Sumudu transform, Therm. Sci, 19(2015), 4, pp.1167-1171
[21] He, J.H., Li, Z.B., Converting fractional differential equations into partial differential equations, Therm. Sci. 16(2012), pp. 331-334.
[22] Li, Z., He, J.H., Fractional complex transform for fractional differential equations, Math. Comput. Appl. 15(2010), pp. 970-973.
[23] Li, Z. B., et al., Exact solutions of time-fractional heat conduction equation by the fractional complex transform, Therm. Sci. 16(2012), pp. 335-338.
[24] Liu, F. J. et al., He’s Fractional Derivative for Heat Conduction in a Fractal Medium Arising in Silkworm Cocoon Hierarchy, Thermal Science, 19 (2015), 4, pp. 1155-1159.
[25] He, J.H. et al,.Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus. Phys. Lett. A 376(2012),pp.257-259.