THERMAL SCIENCE

International Scientific Journal

Yinhong Xia

APPROXIMATE SOLUTION FOR FRACTIONAL BURGERS EQUATION WITH VARIABLE COEFFICIENT USING DAFTARDAR-GEJJI-JAFARIS METHOD

ABSTRACT
A fractional Burgers equation with variable coefficients is studied, which can describe heat conduction in nanomaterials with intermittent property. The equation is solved analytically by Daftardar-Gejji-Jafaris method.
KEYWORDS
fractional Burgers equations, variable coefficients, caputo fractional derivative, Daftardar-Gejji-Jafaris method
PAPER SUBMITTED: 2016-08-25
PAPER REVISED: 2017-08-23
PAPER ACCEPTED: 2017-08-27
PUBLISHED ONLINE: 2018-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI1804607X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE No. 4, PAGES [1607 - 1611]
REFERENCES
[1] Kutluay, S., et al. Numerical Solutions of the Burgers Equation by the Least-Squares Quadratic B-Spline Finite Element Method, Journal of Computational and Applied Mathematics, 167 (2004), 1, pp. 21-33, 10.1016/j.cam.2003.09.043
[2] Wazwaz, A. M., Multiple-Front Solutions for the Burgers Equation and the Coupled Burgers Equations, Applied Mathematics and Computation, 190 (2007), 2, pp. 1198-1206, 10.1016/j.amc.2007.02.003
[3] Musha, T., et al. Traffic Current Fluctuation and the Burgers Equation, Japanese Journal of Applied Physics, 17 (1978), 5, pp. 811, 10.1143/jjap.17.811
[4] Dag, I., et al., A Numerical Solution of the Burgers Equation Using Cubic B-splines. Applied Mathemat-ics and Computation, 163 (2005), 1, pp. 199-211, 10.1016/j.amc.2003.07.027
[5] Sugimoto, N. Burgers Equation with A Fractional Derivative; Hereditary Effects on Nonlinear Acoustic Waves, Journal of Fluid Mechanics, 225 (1991), Apr., pp. 631-653
[6] Abbasbandy, S., Darvishi, M. T., A Numerical Solution of Burgers Equation by Modified Adomian Method, Applied Mathematics and Computation, 163 (2005), 3, pp. 1265-1272, 10.1016/j.amc.2004.04.061
[7] Kenyon, R., Okounkov, A., Limit Shapes and the Complex Burgers Equation, Acta Mathematica, 199 (2007), 2, pp. 263-302, 10.1007/s11511-007-0021-0
[8] Lu, D. C., et al., Backlund Transformation and N-Soliton-Like Solutions to the Combined KdV-Burgers Equation with Variable Coefficients, International Journal of Nonlinear Science, 2 (2006), 1, pp. 3-10
[9] Aksan, E. N., Ozdeş, A., A Numerical Solution of Burgers Equation, Applied Mathematics and Compu-tation, 156 (2004), 2, pp. 395-402
[10] Dogan, A. A., Galerkin Finite Element Approach to Burgers Equation, Applied Mathematics and Com-putation, 157 (2004), 2, pp. 331-346, 10.1016/j.amc.2003.08.037
[11] Helal, M. A., Mehanna, M. S., A Comparison between Two Different Methods for Solving KdV-Burgers Equation, Chaos, Solitons & Fractals, 28 (2006), 2, pp. 320-326, 10.1016/j.chaos.2005.06.005
[12] Kadalbajoo, M. K., Awasthi, A., A Numerical Method Based on Crank-Nicolson Scheme for Burgers Equation, Applied Mathematics and Computation, 182 (2006), 2, pp. 1430-1442, 10.1016/j.amc.2006.05.030
[13] Cui, M., Geng F., A Computational Method for Solving One-Dimensional Variable-Coefficient Burgers Equation, Applied Mathematics and Computation, 188 (2007), 2, pp. 1389-1401, 10.1016/j.amc.2006.11.005
[14] Sophocleous, C., Transformation Properties of A Variable-Coefficient Burgers Equation, Chaos, Soli-tons & Fractals, 20 (2004), 5, pp. 1047-1057, 10.1016/j.chaos.2003.09.024
[15] Daftardar-Gejji, V., Jafari, H., 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
[16] Bhalekar, S., Daftardar-Gejji, V., 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
[17] Daftardar-Gejji, V., Bhalekar, S., 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
[18] He, J.-H., Variational Iteration Method - A Kind of Non-Linear Analytical Technique: Some Examples, International Journal of Nonlinear Mechanics, 34 (1999), 4, pp. 699-708, 10.1016/s0020-7462(98)00048-1
[19] He, J.-H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135 (2003), 1, pp. 73-79, 10.1016/s0096-3003(01)00312-5
[20] 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
[21] Sari, M., et al. A Solution to the Telegraph Equation by Using DGJ Method, International Journal of Nonlinear Science, 17 (2014), 1, pp. 57-66
[22] Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus. Thermal Science, 20 (2016), 3, pp. 773-777, 10.2298/tsci1603773h
[23] Wazwaz, A. M., Gorguis, A., Exact Solutions for Heat-Like and Wave-Like Equations with Variable Coefficients, Applied Mathematics and Computation, 149 (2004), 1, pp. 15-29, 10.1016/s0096-3003(02)00946-3
[24] Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathemati-cal Analysis and Applications, 135 (1988), 2, pp. 501-544, 10.1016/0022-247x(88)90170-9
[25] Elsaid, A., Fractional Differential Transform Method Combined with the Adomian Polynomials, Applied Mathematics and Computation, 218 (2012), 12, pp. 6899-6911, 10.1016/j.amc.2011.12.066
[26] Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000, 10.1142/3779
[27] Oldham, K., Spanier, J., The Fractional Calculus Theory and Applications of Differentiation and Inte-gration to Arbitrary Order, Vol. 111. Elsevier, Amsterdam, The Netherlands, 1974, 10.1016/s0076-5392(09)x6012-1
PDF VERSION [DOWNLOAD]
Approximate solution for fractional Burgers equation with variable coefficient using Daftardar-Gejji-Jafaris method

© 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