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A NEW METHOD SOLVING LOCAL FRACTIONAL DIFFERENTIAL EQUATIONS IN HEAT TRANSFER

ABSTRACT
In this article, a new method, which is coupled by the variational iteration and reduced differential transform method, is proposed to solve local fractional differential equations. The advantage of the method is that the integral operation of variational iteration is transformed into the differential operation. One test examples is presented to demonstrate the reliability and efficiency of the proposed method.
KEYWORDS
PAPER SUBMITTED: 2018-09-12
PAPER REVISED: 2018-11-01
PAPER ACCEPTED: 2018-12-21
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180912237Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 3, PAGES [1663 - 1669]
REFERENCES
  1. Yang, X. J., General Fractional Derivatives: Theory, Methods and Applications, New York, CRC Press, 2019
  2. Kolwankar, K. M., et al., Fractional Differentiability of Nowhere Differentiable Functions and Dimensions, Chaos, 6 (1996), 4, pp.505-513
  3. Babakhani, A., et al., On Calculus of Local Fractional Derivatives. J.Math. Anal. Appl, 270(2002), 1, pp.66-79
  4. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, New York, Academic Press, 2015
  5. Yang, X. J., Advanced Local Fractional Calculus and Its Applications. World Science publisher, New York, 2012
  6. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), Jan., pp.285-296
  7. He, J. H., et al., Local Fractional Variational Iteration Method for Fractal Heat Transfer in Silk Cocoon Hierarchy, Nonlinear Science Letters A.,4(2013),1, pp.15-20
  8. Yang, X. J., et al., On a Fractal LC-electric Circuit Modeled by Local Fractional Calculus, Communications in Nonlinear Science and Numerical Simulation, 47(2017), Jun., pp.200-206
  9. Yang, X. J., et al., New Rheological Models within Local Fractional Derivative Romanian Reports in Physics, 69 (2017), 3, pp.1-8
  10. Hemeda, A. A., et al., Local Fractional Analytical Methods for Solving Wave Equations with Local Fractional Derivative, Mathematical Methods in the Applied Sciences, 41(2018), 6, pp.2515-2529
  11. Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67(2015),3, pp.752-761
  12. Su, W. H., et al., Fractional Complex Transform Method for Wave Equations on Cantor Sets within Local Fractional Differential Operator, Advances in Difference Equations, 2013 (2013), 1, pp.97-105
  13. Yang, X. J., et al., New Analytical Solutions for Klein-Gordon and Helmholtz Equations in Fractal Dimensional Space, Proceedings of the Romanian Academy Series A, Mathematics Physics Technical Sciences Information Science, 18 (2017), 3, pp.231-238
  14. Goswami, P., Solutions of Fractional Differential Equations by Sumudu Transform and Variational Iteration Method, Journal of Nonlinear Science & Applications, 9(2016), 4, pp.1944-1951
  15. Usta, F., et al., Yang-Laplace Transform Method Volterra and Abel's Integro-differential Equations of Fractional Order, International Journal of Nonlinear Analysis and Applications, 9(2018), 2, pp.203-214
  16. Zhao, D, et al., An Efficient Computational Technique for Local Fractional Heat Conduction Equations in Fractal Media, Journal of Nonlinear Sciences and Applications, 10(2017), pp.1478-1486
  17. Singh, J., et al., A Reliable Algorithm for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow, Entropy, 18(2016), 6, pp.1-8
  18. Kumar, et al., A Hybrid Computational Approach for Klein- Gordon Equations on Cantor Sets, Nonlinear Dynamics, 87(2017), 1, pp.511-517
  19. Jafari, H., et al., Reduced Differential Transform Method for Partial Differential Equations within Local Fractional Derivative Operators, Advances in Mechanical Engineering, 8(2016), 4, pp.1-8
  20. Odibat, Z. M., A Study on the Convergence of Variational Iteration Method, Mathematical and Computer Modelling, 51(2010), 9, pp.1181-1192

© 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