THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Bin Chen

,

Lei Chen

,

Zhong-Ze Xia

HE-LAPLACE METHOD FOR TIME FRACTIONAL BURGERS-TYPE EQUATIONS

ABSTRACT
The time fractional Burgers-type equations with He's fractional derivative by He-Laplace method. It is a numerical approach coupled the Laplace transformation and HPM. The approximations to the initial value problem with different fractional orders are given without any discretization and complicated computation. Numerical results are provided to confirm its efficiency.
KEYWORDS
time fractional Burgers-type equation, He-Laplace method, approximation
PAPER SUBMITTED: 2021-12-13
PAPER REVISED: 2022-05-05
PAPER ACCEPTED: 2022-05-05
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303947C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [1947 - 1955]
REFERENCES
  1. Dan, D. D., et al., Using Piecewise Reproducing Kernel Method and Legendre Polynomial for Solving a Class of the Time Variable Fractional Order Advection-reaction-diffusion Equation, Thermal Science, 25 (2021), 2B, pp. 1261-1268
  2. Wang, K. L., et al., Physical Insight of Local Fractional Calculus and its Application to Fractional KdV-Burgers-Kuramoto Equation, Fractals, 27 (2019), 7, 1950122
  3. Habib, S., et al., Study of Non-linear Hirota-Satsuma Coupled KdV and Coupled mKdV System with Time Fractional Derivative, Fractals, 29 (2021), 5, 2150108
  4. Lu, J., An Analytical Approach to Fractional Boussinesq-Burges equations, Thermal Science, 24 (2020), 4A, pp. 2581-2588
  5. 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
  6. 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
  7. Anjum, N., et al., Two-scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 2150182
  8. He, J. H., et al., Evans Model for Dynamic Economics Revised, AIMS Mathematics, 6 (2021), 9, pp. 9194-9206
  9. He, J. H., When Mathematics Meets Thermal Science, The Simpler is the Better, Thermal Science, 25 (2021), 3B, pp. 2039-2042
  10. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  11. He, J. H., A Tutorial Review on Fractal Space-time and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), Nov., pp. 3698-3718
  12. Burger, J. M., A Mathematical Model Illustrating the Theory of Turbulence, Advances in Applied Mechanics, 1 (1948), pp. 171-199
  13. Cole, J. D., On a Quasi Linear Parabolic Equations Occurring in Aerodynamics, Quarterly of Applied Mathematics, 9 (1951), 3, pp. 225-236
  14. Esipov, S. E., Coupled Burgers' Equations: a Model of Poly Dispersive Sedimentation, Physical Review E, 52 (1995), 4, pp. 3711-3718
  15. Nee, J., Duan, J., Limit Set of Trajectories of the Coupled Viscous Burgers' Equations, Applied Mathematics Letter, 11 (1998), 1, pp. 57-61
  16. Soliman, A. A., The Modified Extended Tanh-function Method for Solving Burgers-type Equations, Physica A, 361 (2006), 2, pp. 394-404
  17. Khater, A. H., et al., A Chebyshev Spectral Collocation Method for Solving Burgers'-type Equations, Journal of Computational and Applied Mathematics, 222 (2008), 2, pp. 333-350
  18. Yildirim, A., Kelleci, A., Homotopy Perturbation Method for Numerical Solutions of Coupled Burgers Equations with Time- and Space-fractional Derivatives, International Journal of Numerical Methods for Heat & Fluid Flow, 20 (2010), 8, pp. 897-909
  19. Albuohimad, B., Adibi H., On a Hybrid Spectral Exponential Chebyshev Method for Time-fractional Coupled Burgers Equations on a Semi-infinite Domain, Advance in Difference Equations, 1 (2017), 85
  20. Munjam, S.R., Fractional Transform Methods for Coupled System of Time Fractional Derivatives of Non-homogeneous Burgers' Equations Arise in Diffusive Effects, Computational & Applied Mathemat-ics, 38 (2019), 2, 62
  21. Amit, P., et al. Analytic Study for Fractional Coupled Burger's Equations via Sumudu Transform method, Non-linear Engineering, 7 (2018), 4, pp. 323-332
  22. Lu J., Sun Y., Numerical Approaches to Time Fractional Boussinesq-Burges Equations. Fractals, 29 (2021), 8, 2150244
  23. Nadeem, M., Li, F., He-Laplace Method for Non-linear Vibration Systems and Non-linear Wave Equations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1060-1074
  24. Mishra, H. K., Nagar, A. K., He-Laplace Method for Linear and Non-linear Partial Differential Equations, Journal of Applied Mathematics, 2012 (2012), 180315
  25. 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
  26. He, J. H., et al., The Enhanced Homotopy Perturbation Method for Axial Vibration of Strings, Facta Universitatis Series: Mechanical Engineering, 19 (2021), 4, pp. 735-750
  27. He, J.-H., et al., Homotopy Perturbation Method for the Fractal Toda Oscillator, Fractal Fract, 5 (2021), 3, 93
  28. He, C. H., El-Dib, Y. O., A Heuristic Review on the Homotopy Perturbation Method for Non-conservative Oscillators, On-line first, Journal of Low Frequency Noise Vibration and Active Control, 41 (2022), 2, pp. 571-603
  29. Madani, M., et al., On the Coupling of the Homotopy Perturbation Method and Laplace Transformation, Mathematical and Computer Modeling, 53 (2011), 9-10, pp. 1937-1945
  30. Tasa, B., et al., Investigation of the Fractional Coupled Viscous Burgers' Equation Involving Mittag-Leffler Kernel, Physica A: Statistical Mechanics and its Applications, 527 (2019), Aug., 121126
  31. Chen, J. H., et al., Design and Implementation of FPGA-based Taguchi-Chaos-PSO Sun Tracking Sys-tems, Mechatronics, 25 (2015), Feb., pp. 55-64
  32. Chen, C. L., et al., Terminal Sliding Mode Control for Aeroelastic Systems, Non-linear Dynamics, 70 (2012), 3, pp. 2015-2026
  33. Lu, J., et al., Analysis of the Non-linear Differential Equation of the Circular Sector Oscillator by the Global Residue Harmonic Balance Method, Results in Physics, 19 (2020), Dec., 103403
  34. Lu, J., Global Residue Harmonic Balance Method for Strongly Non-linear Oscillator with Cubic and Harmonic Restoring Force, Journal of Low Frequency Noise Vibration and Active Control, 41 (2022), 4, pp. 1402-1410
  35. Chen, B., et al., Numerical Investigation of the Fractal Capillary Oscillator, Journal of Low Frequency Noise Vibration and Active Control, On-line first, doi.org/10.1177/14613484221131245, 2022
  36. Lu, J., Chen, L., Numerical Analysis of a Fractal Modification of Yao-Cheng Oscillator, Results in Phys-ics, 38 (2022), July, 105602
  37. Lu, J., Ma, L., Numerical Analysis of a Fractional Nonlinear Oscillator with Coordinate-Dependent Mass, Results in Physics, 43 (2022), Dec., 106108
  38. Yu, W., et al., Tensorizing GAN with High-Order Pooling for Alzheimer's Disease Assessment, IEEE Transactions on Neural Networks and Learning Systems, 33 (2021), 9, pp. 4945-4959
  39. You, S., et al., Fine Perceptive Gans for Brain MR Image Super-Resolution In Wavelet Domain, IEEE Transactions on Neural Networks and Learning Systems, On-line first, doi.org/10.1109/TNNLS. 2022.3153088, 2022
  40. Hu, S., et al., Bidirectional Mapping Generative Adversarial Networks for Brain MR to PET Synthesis, IEEE Transactions on Medical Imaging, 41 (2021), 1, pp. 145-157
PDF VERSION [DOWNLOAD]
He-Laplace method for time fractional burgers-type equations

© 2024 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