THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Xiu-Fen Gu

,

Qiu-Ya Wang

,

Meng Zhang

,

Yan-Qin Liu

APPROXIMATE SOLUTIONS OF FRACTIONAL NON-LINEAR EVOLUTION EQUATIONS

ABSTRACT
A novel method which is based on variational iteration method, Laplace transform, and homotopy perturbation method is proposed, and this new method is applied to obtain the approximate solution of the fractional non-linear Boussinessq-type equation. The fractional Lagrange multiplier is accurately determined by the Laplace transform and the non-linear term can be easily handled by He’s polynomials. The result demonstrates accuracy and fast convergence of this new algorithm.
KEYWORDS
variational iteration method, laplace transform, homotopy perturbation method, fractional equation, non-linear equation, Caputo derivative
PAPER SUBMITTED: 2013-09-29
PAPER REVISED: 2014-04-30
PAPER ACCEPTED: 2014-07-07
PUBLISHED ONLINE: 2015-01-04
DOI REFERENCE: https://doi.org/10.2298/TSCI1405553G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE Issue 5, PAGES [1553 - 1556]
REFERENCES
  1. Diethelm, K., The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin, Germany, 2010
  2. Duan, J. S., et al., A Review of the Adomian Decomposition Method and its Applications to Fractional Differential Equations, Commun. Fract. Calc., 3 (2012), 2, pp. 73-99
  3. He, J. H., Homotopy Perturbation Method: a New Non-Linear Analytical Technique, Appl. Math. Comput., 135 (2003), 1, pp. 73-79
  4. Wang, S. W., Xu, M. Y., Axial Couette Flow of Two Kinds of Fractional Viscoelastic Fluids in an Annulus, Non-linear Anal. RWA, 10 (2009), 2, pp. 1087-1096
  5. Liu, Y. Q., Ma, J. H., Exact Solutions of a Generalized Multi-Fractional Non-Linear Diffusion Equation in Eadial Symmetry, Commun. Theor. Phys., 52 (2009), 5, pp. 857-861
  6. Liu, Y. Q., Approximate Solutions of Fractional Non-Linear Equations Using Homotopy Perturbation Transformation Method, Abstr. Appl. Anal., 2012 (2012), Article ID 752869
  7. Liu, Y. Q., Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems, Abstr. Appl. Anal., 2012 (2012), Article ID 727031
  8. Wu, G. C., Baleanu, D., Variational Iteration Method for Fractional Calculus - an Universal Approach by Laplace Tranform, Adv. Difference Equa., 18 (2013), pp. 1-9
  9. Khan, Y., Wu, Q. B., Homotopy Perturbation Transform Method for Non-Linear Equations using He's Polynomials, Comput. Math. Appl., 61 (2011), 8, pp. 1963-1967
  10. Odibat, Z. M., Construction of Solitary Solutions for Non-Linear Dispersive Equations by Variational Iteration Method, Phys. Lett. A, 372 (2008), 22, pp. 4045-4052
PDF VERSION [DOWNLOAD]
Approximate solutions of fractional non-linear evolution equations

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence