THERMAL SCIENCE

International Scientific Journal

Jing Pang

,

Yanqing Cheng

,

Zhengxin Liang

,

Yuedong You

AN ANALYTICAL SOLUTION OF FRACTIONAL BURGERS EQUATION

ABSTRACT
Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.
KEYWORDS
fractional partial differential equation, complex infinite sequence solution, nonlinear superposition formula
PAPER SUBMITTED: 2016-06-15
PAPER REVISED: 2016-08-28
PAPER ACCEPTED: 2016-09-04
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160615060P
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1725 - 1731]
REFERENCES
  1. Zhang, X., et al., The Impact of Boundary on the Fractional Advection-Dispersion Equation for Solute Transport in Soil: Defining the Fractional Dispersive Flux with the Caputo Derivatives, Advances in Wa-ter Resources, 30 (2007), 5, pp. 1205-1217
  2. Chen, W. C., Nonlinear Dynamics and Chaos in a Fractional-Order Financial System, Chaos, Solitons and Fractals, 36 (2008), 5, pp. 1305-1314
  3. Wang, Z., Huang, X., et al., Analysis of Nonlinear Dynamics and Chaos in a Fractional Order Financial System with Time Delay, Computers Mathematics with Applications, 62 (2011), 3, pp. 1531-1539
  4. Schiessel, H., et al., Generalized Viscoelastic Models: Their Fractional Equations with Solutions, Jour-nal of Physics A:Mathematical and General, 28 (1995), 23, pp. 6567-6584
  5. Adolfsson, K., et al., Adaptive Discretization of Fractional Order Viscoelasticity Using Sparse Time History, Computer Methods in Applied Mechanics and Engineering, 193 (2004), 42, pp. 4567-4590
  6. Hall, M. G., Barrick, T. R., From Diffusion-Weighted MRI to Anomalous Diffusion Imaging, Magnetic Resonance in Medicine, 59 (2008), 3, pp. 447-455
  7. Bo, T., et al., A Generalized Fractional Sub-Equation Method for Fractional Differential Equations with Variable Coefficients, Physics Letter A, 376 (2012), 38, pp. 2588-2590
  8. Jumarie, G., Modified Riemann-Liouville Derivative and Fractional Taylor Series of Non-Differentiable Functions Further Results, Computers and Mathematics with Applications, 51 (2006), 9-10, pp. 1367-1376
  9. He, J.-H., et al., Exp-Function Method for Nonlinear Wave Equations, Chaos, Solitons & Fractals, 30 (2006), 3, pp. 700-708
  10. Taogetusang., et al., New Application to Riccati Equation, Chin. Phys. B, 19 (2010), 8, ID 080303
  11. He, J.-H., Frontier of Modern Textile Engineering and Short Remarks on some Topics in Physics, Inter-national Journal of Nonlinear Sciences and Numerical Simulation, 11 (2010), 7, pp. 555-563
  12. Huang, J., Liu, H. H., New Exact Travelling Wave Solutions for Fisher Equation and Burgers-Fisher Equation, Journal of Mathematics, 31 (2011), Jan., pp. 631-637
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An analytical solution of fractional burgers equation

© 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