THERMAL SCIENCE

International Scientific Journal

Shu-Xian DengORCID

,

Xin-Xin Ge

APPLICATION OF DGJ METHOD FOR SOLVING NON-LINEAR LOCAL FRACTIONAL HEAT EQUATIONS

ABSTRACT
In this paper, the initial value problem for a new non-linear local fractional heat equation is considered. The fractional complex transform method and the DGJ decomposition method are used to solve the problem, and the approximate analytical solutions are also obtained.
KEYWORDS
nonlinear local fractional heat equation, fractional complex transform method, the DGJ decomposition method
PAPER SUBMITTED: 2018-08-25
PAPER REVISED: 2018-11-09
PAPER ACCEPTED: 2019-02-15
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180825225D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE No. 3, PAGES [1571 - 1576]
REFERENCES
[1] Truman, A., Classical Mechanics, the Diffusion (Heat) Equation, and the Schrödinger Equation. Journal of Mathematical Physics, 12(1977), 18, pp.2308-2315, 10.1063/1.523240
[2] Luo, J., et al., A Reiterated Two-Scale Probabilistic Modeling and Numerical Simulation for Heat Equation in a Fractal Porous Media, Journal of Engineering Thermophysics, 3(2003), 34, pp.188-196
[3] Yang, A. M., et al., Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative, Abstract and Applied Analysis, 2(2014), 2014, pp.1-5, 10.1155/2014/395710
[4] Tarasov, V. E., Vector Calculus in Non-Integer Dimensional Space and Its Applications to Fractal Media, Communications in Nonlinear Science and Numerical Simulation, 2(2015), 20, pp.360-374, 10.1016/j.cnsns.2014.05.025
[5] Yang, X.-J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 2017,151(1-4), pp. 63-75, 10.3233/fi-2017-1479
[6] Yang, X.-J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 2017, 69(3),113
[7] Yang, X.-J., et al., Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-De Vries Equation (Public Access), Abstract and Applied Analysis, 2014, 2014, 278672
[8] H. Jafari., et al., Local Fractional Series Expansion Method for Solving Laplace and Schrodinger Equations on Cantor Sets within Local Fractional Operators, International Journal of Mathematics and Computer Research,11(2014), 2, pp.736-744
[9] Alkhasov, A. B., et al., Heat Conduction Equation in Fractional-Order Derivatives, Journal of Engineering Physics and Thermophysics, 2(2011), 84, pp.332-341, 10.1007/s10891-011-0477-9
[10] Yang, X.-J., Local Fractional Partial Differential Equations with Fractal Boundary Problems, Advances in Computational Mathematics and Its Applications, 1(2012),1, pp. 60-63
[11] Yang, X.-J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 2 (2013), 17, pp.625-628, 10.2298/tsci121124216y
[12] Baleanu, D., et al., Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets, Abstract and Applied Analysis, Article ID 535048(2014), pp.1-6
[13] Wang, S. Q., et al., Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, Article ID 176395(2014), pp.1-7, 10.1155/2014/176395
[14] Su, W. H., Fractional Complex Transform Method for Wave Equations on Cantor Sets within Local Fractional Differential Operator, Advances in Difference Equations, 1(2013), 2013, pp.1-8, 10.1186/1687-1847-2013-97
[15] Zayed, E. M. E., et al., The Fractional Complex Transformation for Nonlinear Fractional Partial Differential Equations in The Mathematical Physics, Journal of the Association of Arab Universities for Basic and Applied Sciences, 1(2016), 19, pp.59-69, 10.1016/j.jaubas.2014.06.008
[16] Daftardar-Gejji., et al., An Iterative Method for Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications, 316(2006), 2, pp.753-763, 10.1016/j.jmaa.2005.05.009
[17] Bhalekar, S., et al., New Iterative Method: Application to Partial Differential Equations, Applied Mathematics and Computation, 203(2008), 2, pp.778-783, 10.1016/j.amc.2008.05.071
[18] Daftardar-Gejji., et al., Solving Fractional Boundary Value Problems with Dirichlet Boundary Conditions Using a New Iterative Method, Computers & Mathematics with Applications, 59(2010), 5, pp.1801-1809, 10.1016/j.camwa.2009.08.018
[19] Jaradata, H. M., et al., A New Numerical Method for Heat Equation Subject to Integral Specifications, Journal of Nonlinear Science and Applications, 5(2016), 9, pp.2117-2125, 10.22436/jnsa.009.05.17
[20] Kot, V. A., Multiple Integration of the Heat-Conduction Equation for a Space Bounded from the Inside, Journal of Engineering Physics and Thermophysics ,2(2016), 89, pp.369-390, 10.1007/s10891-016-1387-7
[21] Khader, M. M., Application of Homotopy Perturbation Method for Solving Nonlinear Fractional Heat-Like Equations Using Sumudu Transform, Scientia Iranica, 2(2017), 24, pp.648-655
[22] Çelik, C., et al., Finite Element Method for a Symmetric Tempered Fractional Diffusion Equation, Applied Numerical Mathematics, 20(2017), 1, pp.270-286
[23] Bahrami, F., et al., On the Invariant Solutions of Space Time Fractional Diffusion Equations, Indian Journal of Physics, 1(2017), 1, pp.1-9
[24] Wen, Y. X., et al., Exact Solutions for the Generalized Nonlinear Heat Conduction Equations Using the Exp-Function Method, Computers and Mathematics with Applications, 11(2009), 58, pp.2464-2467, 10.1016/j.camwa.2009.03.037
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Application of DGJ method for solving non-linear local fractional heat equations

© 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