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LOCAL FRACTIONAL DERIVATIVE: A POWERFUL TOOL TO MODEL THE FRACTAL DIFFERENTIAL EQUATION

ABSTRACT
In this paper, the modified Fornberg-Whitham equation is described by the local fractional derivative for the first time. The fractal complex transform and the modified reduced differential transform method are successfully adopted to solve the modified local Fornberg-Whitham equation defined on fractal sets.
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PAPER SUBMITTED: 2018-07-12
PAPER REVISED: 2018-09-13
PAPER ACCEPTED: 2019-01-28
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180712243Y
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THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 3, PAGES [1703 - 1706]
REFERENCES
  1. Whitham, G. B., Variational Methods and Applications to Water Wave, Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences, 299(1967), pp.6-25
  2. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  3. Yang, X. J., et al., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communication in Nonlinear Science and numerical Simulation ,29(2015), pp. 499-504
  4. Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 8,pp.1-8
  5. Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers-Type Equations, Computers and Mathematics with Applications, 73 (2017), 2, pp.203-210
  6. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), pp.285-296
  7. Yang, X. J., et al., Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25(2017), 4, pp.1-6
  8. Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Report Physics, 67 (2015), 3,pp.752-761
  9. Kumar, D., et al., A Hybrid Computational Approach for Klein-Gordon Equations on Cantor Sets, Nonlinear Dynamics, 87(2017), 1,pp.511-517
  10. Anastassiou, G., et al., Local Fractional Integrals Involving Generalized Strongly M-convex Mappings, Arabian Journal of Mathematics, 2018,pp.1-13
  11. Ziane, D., et al., Local Fractional Sumudu Decomposition Method for Linear Partial Differential Equations with Local Fractional Derivative, Journal of King Saud University - Science, 31 (2017) ,pp.83-88
  12. Li, Z. B., et al., Fractional Complex Transform for Fractional Differential Equations, Mathematical Computational Application,15(2010), pp. 970-973
  13. Wang, K.L., et al., Analytical Study of Time-Fractional Navier-Stokes Equation by Using Transform Methods, Advances in Difference Equations,2016, 2016(61), pp.1-12

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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