THERMAL SCIENCE

International Scientific Journal

Shuxian DengORCID

,

Zihao Deng

APPROXIMATE ANALYTICAL SOLUTIONS FOR A CLASS OF GENERALIZED PERTURBED KDV-BURGERS EQUATION

ABSTRACT
In this paper, we establish an efficient algorithm for solving a class of generalized perturbed KdV-Burgers equation with conformable time fractional derivative and He's space fractal derivative. An illustrative example is presented.
KEYWORDS
the generalized perturbed KdV-Burgers equation, Adomian decomposition method, He’s space fractal derivative, the conformable fractional derivative
PAPER SUBMITTED: 2020-08-05
PAPER REVISED: 2022-07-16
PAPER ACCEPTED: 2022-07-16
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303881D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE No. 3, PAGES [1881 - 1888]
REFERENCES
[1] Jawad, A. J. M., et al., Soliton Solutions of Burgers Equations and Perturbed Burgers Equation, Applied Mathematics and Computation, 216 (2010), 11, pp. 3370-3377, 10.1016/j.amc.2010.04.066
[2] Yu, J., et al., Dynamical Behavior in the Perturbed Compound KdV-Burgers Equation, Chaos Solitons and Fractals, 33 (2007), 4, pp. 1307-1313, 10.1016/j.chaos.2006.01.107
[3] Kudryashov, N. A., Sinelshchikov, D. I., Periodic Structures Described by the Perturbed Burgers-Korteweg-de Vries Equation, International Journal of Non-Linear Mechanics, 72 (2015), 10, pp. 16-22, 10.1016/j.ijnonlinmec.2015.02.008
[4] Deng, S. X., Ge, X. X. Analytical Solution to Local Fractional Landau-Ginzburg-Higgs Equation on Fractal Media, Thermal Science, 25 (2021), 6B, pp. 4449-4455, 10.2298/tsci2106449d
[5] Dong, M., et al., A New RLC Series-Resonant Circuit Modeled by Local Fractional Derivative, Thermal Science, 25 (2021), 6B, pp. 4569-4576, 10.2298/tsci2106569d
[6] Gao, F., Chi, C., Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations, Journal of Function Spaces, 2020 (2020), Aug., 5852414, 10.1155/2020/5852414
[7] Hashemi, S. M., Invariant Subspaces Admitted by Fractional Differential Equations with Conformable Derivatives, Chaos Solitons and Fractals, 107 (2018), Feb., pp. 161-169, 10.1016/j.chaos.2018.01.002
[8] Abdeljawad, T., et al., Fractional logistic models in the frame of fractional operators generated by con-formable derivatives, Chaos, Solitons and Fractals, 119 (2019), 1, pp. 94-101., 10.1016/j.chaos.2018.12.015
[9] Meng, F.W., et al., Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method, Advances in Mathematical Phys-ics, 2018 (2018), 4596506, 10.1155/2018/4596506
[10] Iyiola, O. S., Nwaeze, E. R., Some New Results on the New Conformable Fractional Calculus with Application Using D'Alambert Approach, Progress in Fractional Differentiation and Applications, 2 (2016), 2, pp. 115-122, 10.18576/pfda/020204
[11] Qian, M. Y., et al., Two-Scale Thermal Science for Modern Life -Making the Impossible Possible, Thermal Science, 26 (2022), 3B, pp. 2409-2412, 10.2298/tsci2203409q
[12] He, J. H., Seeing with a Single Scale is Always Unbelieving: From Magic to Two-Scale Fractal, Thermal Science, 25 (2021), 2B, pp. 1217-1219, 10.2298/tsci2102217h
[13] He, J. H., El-Dib, Y. O., A Tutorial Introduction to the Two-scale Fractal Calculus and its Application to the Fractal Zhiber-Shabat Oscillator, Fractals, 29 (2021), 8, 2150268, 10.1142/s0218348x21502686
[14] 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
[15] Tian, D., et al. Fractal N/MEMS: from Pull-In Instability to Pull-In Stability, Fractals, 29 (2021), 2, 2150030, 10.1142/s0218348x21500304
[16] He, C. H., et al., A Fractal Model for the Internal Temperature Response of a Porous Concrete, Applied and Computational Mathematics, 21 (2022), 1, pp. 71-77
[17] He, C. H., A Variational Principle for a Fractal Nano/Microelectromechanical (N/MEMS) System, International Journal of Numerical Methods for Heat & Fluid Flow, 33 (2022), 1, pp. 351-359, 10.1108/hff-03-2022-0191
[18] He, C. H., et al., A Modified Frequency-Amplitude Formulation for Fractal Vibration Systems, Fractals, 30 (2022), 3, 2250046, 10.1142/s0218348x22500463
[19] Shen, Y., El-Dib, Y. O., A Periodic Solution of the Fractional Sine-Gordon Equation Arising in Architectural Engineering, Journal of Low Frequency Noise, Vibration & Active Control, 40 (2021), 2, pp. 683-691, 10.1177/1461348420917565
[20] Liu, F. J., et al., Thermal Oscillation Arising in a Heat Shock of a Porous Hierarchy and Its Application, Facta Universitatis Series: Mechanical Engineering, 20 (2021), 3, pp. 633-645, 10.22190/fume210317054l
[21] Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics，Fractals, 29 (2021), 7, 2150182, 10.1142/s0218348x21501826
[22] He, J. H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6 (2021), 9, pp. 9194-9206, 10.3934/math.2021534
[23] He, J. H., et al., Variational Approach to Fractal Solitary Waves, Fractals, 29 (2021), 7, 2150199, 10.1142/s0218348x21501991
[24] He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and its Fractal Variational Principle, International Journal of Modern Physics B, 35 (2021), 21, 2150214, 10.1142/s0217979221502143
[25] Guedria, N., et al., A Direct Algebraic Method for Eigensolution Sensitivity Computation of Damped Asymmetric Systems, International Journal for Numerical Methods in Engineering, 68 (2010), 6, pp. 674-689, 10.1002/nme.1732
[26] Yan,W. J., et al., A Direct Algebraic Method to Calculate the Sensitivity of Element Modal Strain Energy, International Journal for Numerical Methods in Biomedical Engineering, 27 (2011), 5, pp. 694-710, 10.1002/cnm.1322
[27] Seadawy, A. R., The Solutions of the Boussinesq and Generalized Fifth-Order KdV Equations by Using the Direct Algebraic Method, Applied Mathematical Sciences, 82 (2012), 6, pp. 4081-4090
[28] Elwakil, S. A., et al., Modified Extended Tanh-Function Method and Its Applications to Non-linear Equations, Applied Mathematics and Computation, 161 (2005), 2, pp. 403-412, 10.1016/j.amc.2003.12.035
[29] Anjum, N., He, J. H., Analysis of Non-Linear Vibration of Nano/Microelectromechanical System Switch Induced by Electromagnetic Force Under Zero Initial Conditions, Alexandria Engineering Journal, 59 (2020), 6, pp. 4343-4352, 10.1016/j.aej.2020.07.039
[30] Skrzypacz, P., et al., A Simple Approximation of Periodic Solutions to Microelectromechanical System Model of Oscillating Parallel Plate Capacitor, Mathematical Methods in Applied Sciences, On-line first, , 2020, 10.1002/mma.6898
[31] Fan, E. G., Zhang,J., Applications of the Jacobi Elliptic Function Method to Special-Type Non-linear equations, Physics Letters A, 305 (2002), 6, pp. 383-392, 10.1016/s0375-9601(02)01516-5
[32] Anjum, N., et al., Li-He's Modified Homotopy Perturbation Method for Doubly-Clamped Electrically Actuated Microbeams-Based Microelectromechanical System, Facta Universitatis Series: Mechanical Engineering 19 (2021), 4, pp. 601- 612, 10.22190/fume210112025a
[33] He, J. H., El-Dib, Y. O., The Enhanced Homotopy Perturbation Method for Axial Vibration of Strings, Facta Universitatis Series: Mechanical Engineering, 19 (2021), 4, pp. 735-750, 10.22190/fume210125033h
[34] He, J.-H., et al., Homotopy Perturbation Method for the Fractal Toda Oscillator. Fractal Fract., 5 (2021), 3, 5030093, 10.3390/fractalfract5030093
[35] Hashim, I., et al., Solving the Generalized Burgers-Huxley Equation Using the Adomian Decomposition Method, Mathematical and Computer Modelling, 11-12 (2006), 43, pp. 1404-1411, 10.1016/j.mcm.2005.08.017
[36] Hashim, I., et al., Accuracy of the Adomian Decomposition Method Applied to the Lorenz System, Chaos Solitons and Fractals, 5 (2006), 28, pp. 1149-1158, 10.1016/j.chaos.2005.08.135
[37] Ozgumus, O. O., Kaya, M. O., Flapwise Bending Vibration Analysis of Double Tapered Rotating Euler-Bernoulli Beam by Using the Differential Transform Method, Meccanica, 6 (2006), 41, pp. 661-670, 10.1007/s11012-006-9012-z
[38] Cui, R.Q., Hu, Y., Fractional Power Series Method for Solving Fractional Differemtial Equation, Journal of Advances in Mathematics, 4 (2016), 12, pp. 6156-6159, 10.24297/jam.v12i4.360
[39] Mohyud-Din, S., et al., Travelling Wave Solutions of Seventh-Order Generalized KdV Equations Using He's Polynomials, International Journal of Non-linear Sciences and Numerical Simulation, 10 (2009), 2, pp. 223-229, 10.1515/ijnsns.2009.10.2.227
[40] Shokhanda, R., et al., An Approximate Solution of the Time-Fractional Two-Mode Coupled Burgers Equation, Fractal and Fractional, 5 (2021), 4, 196, 10.3390/fractalfract5040196
PDF VERSION [DOWNLOAD]
Approximate analytical solutions for a class of generalized perturbed KdV-burgers 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