THERMAL SCIENCE

International Scientific Journal

Yan WangORCID

,

Yu-Feng ZhangORCID

,

Zhen-Jiang LiuORCID

AN EXPLANATION OF LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD AND ITS APPLICATION TO LOCAL FRACTIONAL MKDV EQUATION

ABSTRACT
The variational iteration method was originally proposed to solve nonlinear problems of differential equations, this paper shows that it is also a powerful mathematical tool to local fractional differential equations. Two local fractional mKdV equations are used as examples to reveal the simple solution process.
KEYWORDS
mKdV equation, local fractional derivative, local fractional variational iteration method, series solution
PAPER SUBMITTED: 2016-05-01
PAPER REVISED: 2016-08-28
PAPER ACCEPTED: 2016-12-29
PUBLISHED ONLINE: 2017-06-04
DOI REFERENCE: https://doi.org/10.2298/TSCI160501143W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE No. 1, PAGES [23 - 27]
REFERENCES
[1] He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014),11, pp.3698-3718, 10.1007/s10773-014-2123-8
[2] Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, NY, USA, 2015, 10.1016/c2014-0-04768-5
[3] Yang, X. J., et al., On Exact Traveling-wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 084312, pp.1-5, 10.1063/1.4960543
[4] Hu, Y., et al., On Fractal Space-time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp.773-777, 10.2298/tsci1603773h
[5] Guner, O., Bekir, A., Exp-function Method for Nonlinear Fractional Differential Equations, Nonlinear Sci. Lett. A, 8 (2017), 1, pp.41-49
[6] Zhang, S., et al., A Direct Algorithm of Exp-function Method for Nonlinear Evolution Equations in Fluids, Thermal Science, 20 (2016), 33, pp.881-884, 10.2298/tsci1603881z
[7] Khaleghizadeh, S., On Fractional Sub-equation Method, Nonlinear Sci. Lett. A, 8 (2017), 1, pp.66-76, 10.1002/9781119697060.ch23
[8] Rajeev, Singh, A. K., Homotopy Analysis Method for a Fractional Stefan Problem, Nonlinear Sci. Lett. A, 8 (2017), 1, pp.50-59
[9] Zhuang, J. Y., et al., The Method of Separation of Variables for Local Fractional Korteweg-de Vries Equation, Thermal Science, 20 (2016), Suppl.3, pp.859-862, 10.2298/tsci16s3859z
[10] Zhang, W., et al., The Local Fractional Series Expansion Solution for Local Fractional Korteweg-de Vries Equation, Thermal Science, 20 (2016), Suppl.3, pp.863-866, 10.2298/tsci16s3863z
[11] Ye, S. S., et al., The Laplace Series Solution for Local Fractional Korteweg-de Vries Equation, Thermal Science, 20 (2016), Suppl.3, pp.867-870, 10.2298/tsci16s3867y
[12] Li, Z. B., He, J. H., Exact Solutions of Time-fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338, 10.2298/tsci110503069l
[13] 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, 10.2298/tsci1504155l
[14] Liu, F. J., et al., A Fractional Model for Insulation Clothings with Cocoon-like Porous Structure, Thermal Science, 20 (2016), 3, pp.779-784, 10.2298/tsci1603779l
[15] He, J. H., Variational Iteration Method-a Kind of Non-linear Analytical Technique: Some Examples, International Journal of Non-Linear Mechanics, 34 (1999), 4, pp.699-708, 10.1016/s0020-7462(98)00048-1
[16] Wu, G. C., Lee, E. W. M., Fractional Variational Iteration Method and its Application. Physics Letters A ,374 (2010), 25, pp.2506-2509, 10.1016/j.physleta.2010.04.034
[17] He, J. H., A Short Remark on Fractional Variational Iteration Method, Physics Letters A, 375 (2011), 38, pp.3362-3364, 10.1016/j.physleta.2011.07.033
[18] Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method , Thermal Science, 2 (2013), 17, pp.625-628, 10.2298/tsci121124216y
[19] He, J. H., Liu, F. J., Local Fractional Variational Iteration Method for Fractal Heat Transfer in Silk Cocoon Hierarchy, Nonlinear Science Letters A, 4 (2013),1, pp.15-20
[20] Meng, Z. J., et al., Local Fractional Variational Iteration Algorithm III for the Diffusion Model Associated with Non-differential Heat Transfer, Thermal Science, 20 (2016), Supp.3, pp. S781-S784
[21] Lu, J. F., Ma, L., Analytical Approach to a Generalized Hirota-Satsuma Coupled Korteweg-de Vries Equation by Modified Variational Iteration Method, Thermal Science, 20 (2016), 3, pp.885-888, 10.2298/tsci1603885l
[22] He, J. H., A Tutorial and Heuristic Review on Lagrange Multiplier for Optimal Problems, Nonlinear Science Letters A, 8 (2017), 2, pp. 121-148
[23] Hojat, A., et al., On Mittag-Leffler Function and Beyond, Nonlinear Science Letters A, 8 (2017), 2, pp.187-199
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An explanation of local fractional variational iteration method and its application to local fractional mKdV equation

© 2026 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