THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

GENERALIZED EXP-FUNCTION METHOD FOR NON-LINEAR SPACE-TIME FRACTIONAL DIFFERENTIAL EQUATIONS

ABSTRACT
A generalized exp-function method is proposed to solve non-linear space-time fractional differential equations. The basic idea of the method is to convert a fractional partial differential equation into an ordinary equation with integer order derivatives by fractional complex transform. To illustrate the effectiveness of the method, space-time fractional asymmetrical Nizhnik-Novikor-Veselov equation is considered. The fractional derivatives in the present paper are in Jumarie’s modified Riemann-Liouville sense.
KEYWORDS
PAPER SUBMITTED: 2014-03-08
PAPER REVISED: 2014-05-12
PAPER ACCEPTED: 2014-07-02
PUBLISHED ONLINE: 2015-01-04
DOI REFERENCE: https://doi.org/10.2298/TSCI1405573Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE Issue 5, PAGES [1573 - 1576]
REFERENCES
  1. He, J. H., Homotopy Perturbation Method: A New Non-linear Analytical Technique, Applied Mathematics and Computation, 135 (2003), 1, pp. 73-79
  2. Yan, L. M., Modified Homotopy Perturbation Method Coupled with Laplace Transform for Fractional Heat Transfer and Porous Media Equations, Thermal Science, 17 (2013), 5, pp. 1409-1414
  3. He, J. H., Wu, X. H., Variational Iteration Method: New Development and Applications, Computers and Mathematics with Applications, 54 (2007), 7-8, pp. 881-894
  4. Zhang, S., Zhang, H. Q., Fractional Sub-Equation Method and Its Applications to Non-linear Fractional PDES, Physics Letters A, 375 (2011), 7 , pp. 1069-1073
  5. Liu, Y. Q., Yan, L. M., Solutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov- Veselov Equations Using a Generalized Fractional Subequation Method, Abstract and Applied Analysis, 2013 (2013), Article ID 839613
  6. Jafari, H., et al., A New Approach for Solving a System of Fractional Partial Differential Equations, Computers and Mathematics with Applications, 66 (2013), 5, pp. 838-843
  7. Yan, L. M., Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method, Abstract and Applied Analysis, 2013 (2013), Article ID 465160
  8. He, J. H., Exp-Function Method for Non-linear Wave Equations, Chaos, Solitons and Fractals, 30 (2006), 3, pp. 700-708
  9. Jumarie, G., Modified Riemann-Liouville Derivative and Fractional Taylor Series of Nondifferentiable Functions Further Results, Computers and Mathematics with Applications, 51 (2006), 9-10, pp. 1367- 1376
  10. Zhang, L. H., et al., Symmetry, Reductions and New Solutions of ANNV Equation through Lax Pair, Communications in Theoretical Physics, 50 (2008), 1, pp. 1-6

© 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