THERMAL SCIENCE

International Scientific Journal

Yi TianORCID

,

Jian-Xiong Wan

EXACT SOLUTIONS OF SPACE-TIME FRACTIONAL (2+1)-DIMENSIONAL BREAKING SOLITON EQUATION

ABSTRACT
This paper suggests a direct algebraic method for finding exact solutions of the space-time fractional (2+1)-dimensional breaking soliton equation. The solution procedure is reduced to solve a large system of algebraic equations, which is then solved by Wu’s method.
KEYWORDS
Direct algebraic method, Wu’s method, fractional (2+1)-dimensional breaking soliton equation, exp-function method
PAPER SUBMITTED: 2020-04-21
PAPER REVISED: 2020-06-18
PAPER ACCEPTED: 2020-06-18
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200421016T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE No. 2, PAGES [1229 - 1235]
REFERENCES
[1] He, J. H., Homotopy Perturbation Method: A New Non-Linear Analytical Technique, Applied Mathematics and Computation, 135 (2003), 1, pp.73-79, 10.1016/s0096-3003(01)00312-5
[2] Yu, D. N., et al., Homotopy Perturbation Method with an Auxiliary Parameter for Non-Linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1540-1554, 10.1177/1461348418811028
[3] Kuang, W. X., et al., Homotopy Perturbation Method with an Auxiliary Term for the Optimal Design of a Tangent Non-Linear Packaging System, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1075-1080, 10.1177/1461348418821204
[4] He, J. H., Latifizadeh, H., A General Numerical Algorithm for Non-Linear Differential Equations by the Variational Iteration Method, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4797-4810, 10.1108/hff-01-2020-0029
[5] Anjum, N., He, J. H., Laplace Transform: Making the Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138, 10.1016/j.aml.2019.01.016
[6] He, J.H., Jin, X., A Short Review on Analytical Methods for the Capillary Oscillator in a Nanoscale Deformable Tube, Mathematical Methods in the Applied Sciences, On-line first, [doi.org/10.1002/]( mma.6321, 2020, 10.1002/mma.6321
[7] He, J. H., The Simpler, The Better: Analytical Methods for Non-Linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260, 10.1177/1461348419844145
[8] He, J. H., A Short Review on Analytical Methods for to a Fully Fourth Order Non-Linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4933-4934, 10.1108/hff-01-2020-0060
[9] He, J. H., Notes on the Optimal Variational Iteration Method, Applied Mathematics Letters, 25 (2012), 10, pp. 1579-1581, 10.1016/j.aml.2012.01.004
[10] He, J. H., Exp-Function Method for Fractional Differential Equations, International Journal of Non-Linear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366, 10.1515/ijnsns-2011-0132
[11] Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448, 10.1016/j.apm.2020.01.027
[12] He, J. H., et al., Difference Equation vs. Differential Equation on Different Scales, International Journal of Numerical Methods for Heat and Fluid-Flow, On-line first, , 2020, 10.1108/HFF-03-2020-0178
[13] Zhang, S., et al., Simplest Exp-Function Method for Exact Solutions of Mikhauilov-Novikov-Wang Equation, Thermal Science, 23 (2019), 4, pp. 2381-2388, 10.2298/tsci1904381z
[14] 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, 10.1016/j.physleta.2011.11.030
[15] He, J. H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equation, Thermal Science, 16 (2012), 2, pp. 331-334
[16] Li, Z. B., et al., Exact Solution of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338, 10.2298/tsci110503069l
[17] He, J. H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681, 10.2298/tsci200127065h
[18] He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133, 10.2298/tsci1904131h
[19] Ain, Q. T, He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, 2, pp. 1707-1712, 10.2298/tsci190408138a
[20] Choi, J. H., Kim, H., Soliton Solutions for the Space-Time Non-Linear Partial Differential Equations with Fractional-Orders, Chinese Journal of Physics, 55 (2017), 2, pp. 556-565, 10.1016/j.cjph.2016.10.019
[21] Wu, W. T., Mathematics Mechanization, Science Press, Beijing, China, 2000
[22] Rezazadeh, H., et al., New Optical Solitons of Non-Linear Conformable Fractional Schrodinger-Hirota Equation, Optic, 172 (2018), Nov., pp. 545-553, 10.1016/j.ijleo.2018.06.111
[23] Rezazadeh, H., et al., New Exact Solutions of Non-Linear Conformable Time-Fractional Phi-4 Equation, Chinese Journal of Physics, 56 (2018), 6, pp. 2805-2816, 10.1016/j.cjph.2018.08.001
[24] Wang, K. L., Yao, S. W., Numerical Method for Fractional Zakharov-Kuznetsov Equations with He's Fractional Derivative, Thermal Science, 23 (2019), 4, pp. 2163-2170, 10.2298/tsci1904163w
[25] He, J. H., et al., A New Fractional Derivative and Its Application Explanation of Polar Bear Hairs, Journal of King Saud University Science, 28 (2016), 2, pp. 190-192, 10.1016/j.jksus.2015.03.004
[26] He, J. H., Li, Z. B., A Fractional Model for Dye Removal, Journal of King Saud University Science, 28 (2016), 1, pp. 14-16, 10.1016/j.jksus.2015.07.001
[27] 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
[28] Wang, Q. L., et al., Fractal Calculus and Its Application Explanation of Biomechanism of Polar Hairs, 26 (2018), 1850086, Fractals, 27 (2019), 5, 1992001
[29] Wang, Q. L., et al., Fractal Calculus and Its Application Explanation of Biomechanism of Polar Hairs, 26 (2018), 1850086, Fractals, 26 (2018), 6, 1850086
[30] He, J. H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276, 10.1016/j.rinp.2018.06.011
[31] Tian, Y., Wang, K. L., Polynomial Characteristic Method an Easy Approach to Lie Symmetry, Thermal Science, 24 (2020), 4, pp. 2629-2635, 10.2298/tsci2004629t
[32] Tian, Y., Wang, K.-L., Conservation Laws for Partial Differential Equations Based on the Polynomial Characteristic Method, Thermal Science, 24 (2020), 4, pp. 2529-2534, 10.2298/tsci2004529t
[33] Wang, Y., et al., Using Reproducing Kernel for Solving a Class of Fractional Partial Differential Equation with Non-Classical Conditions, Applied Mathematics and Computation, 219 (2013), 11, pp. 5918-5925, 10.1016/j.amc.2012.12.009
[34] Wang, Y., et al. New algorithm for second-order boundary value problems of integro-differential equation, Journal of Computational and Applied Mathematics, 229 (2009), July, pp.1-6, 10.1016/j.cam.2008.10.007
[35] Zhu, L., The Quenching Behavior for a Quasilinear Parabolic Equation with Singular Source and Boundary Flux, Journal of Dynamical and Control Systems, 25 (2019), 4, pp. 519-526, 10.1007/s10883-018-9415-x
[36] Zhu, L., Complete Quenching Phenomenon for a Parabolic p-Laplacian Equation with a Weighted Absorption, Journal of Inequalities and Applications, 2018 (2018), 1, 248, 10.1186/s13660-018-1841-5
PDF VERSION [DOWNLOAD]
Exact solutions of space-time fractional (2+1)-dimensional breaking soliton 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