International Scientific Journal

Authors of this Paper

External Links


In this paper, the reduced differential transform method is modified and successfully used to solve the fractional heat transfer equations. The numerical examples show that the new method is efficient, simple, and accurate.
PAPER REVISED: 2017-10-20
PAPER ACCEPTED: 2017-12-08
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1871 - 1875]
  1. Xiao, C., Li, X. W., Solvability of Nonlinear Sequential Fractional Dynamical Systems with Damping, Journal of Applied Mathematics and Physics, 2 (2017), 5, pp. 303-310
  2. Kumar, S., A New Fractional Modeling Arising in Engineering Sciences and Its Analytical Approximate Solution, Alexandria Engineering Journal, 52 (2013), 4, pp. 813-819
  3. Momain, S., Yildilim, A., Analytical Approximate Solutions of the Fractional Convection-Diffusion Equation with Nonlinear Source Term by He's Homotopy Perturbation Method, International Journal of Computer Mathematics, 87 (2010), 5, pp. 1057-1065
  4. Blasiak, S., Time-Fractional Heat Transfer Equations in Modeling of the Non-Contacting Face Seals, In-ternational Journal of Heat and Mass Transfer, 100 (2016), Sept., pp. 79-88
  5. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  6. He, J.-H., et al., A New Fractional Derivative and Its Application to Explanation of Polar Bear Hairs, Journal of King Saud University Science, 28 (2016), 2, pp. 190-192
  7. He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, Int. J. Theor. Phys, 53 (2014), 11, pp. 3698-3718
  8. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  9. Zhao, D. Z., Luo, M. K., General Conformable Fractional Derivative and Its Physical Interpretation, Calcolo, 54 (2017), 3, pp. 903-917
  10. Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathemati-cal Analysis and Applications, 135 (1988), 2, pp. 501-544
  11. He, J.-H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135 (2003), 1, pp. 73-79
  12. He, J.-H., A Coupling Method of a Homotopy Technique and a Perturbation Technique for Nonlinear Problems, International Journal of Non-Linear Mechanics, 35 (2000), 1, pp. 37-43
  13. He, J.-H., Application of Homotopy Perturbation Method to Nonlinear Wave Equation, Chaos, Solitons & Fractals, 26 (2005), 3, pp. 695-700
  14. Rajeev., Homotopy Perturbation Method for a Stefan Problem with Variable Latent Heat, Thermal Sci-ence, 18 (2014), 2, pp. 391-398
  15. Yang, A. M., et al., Laplace Variational Iteration for the Two-Dimensional Diffusion Equation in Ho-mogeneous Materials, Thermal Science, 19 (2015), Suppl. 1, pp. S163-S168
  16. Lu, J. F., An Analytical Approach to the Fornberg-Whitham Equation Type Equations by Using the Var-iational Iteration Method, Comput. Math. Applicat., 61 (2011), 8, pp. 2010-2013
  17. He, J.-H., Variational Iteration Method - Some Recent Results and New Interpretations, J. Comput. Appl. Math., 207 (2007), 1, pp. 3-17
  18. Lin, J., Lu, J. F., Variational Iteration Method for the Classical D-Sokolov-Wilson Equation, Thermal Science, 18 (2014), 5, pp. 1543-1546
  19. Liao, S. J., Chwang, A. T., Application of Homotopy Analysis Method in Nonlinear Oscillations, Jour-nal of Applied Mechanics, 65 (1998), 4, pp. 914-922
  20. Wazwaz, A. M., A Comparison Between Adomian Decomposition Method and Taylor Series Method in the Series Solutions, Applied Mathematics & Computation, 97 (1998), 1, pp. 37-44
  21. Daftardar, G., Hossein, J., An Iterative Method for Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications, 316 (2006), 2, pp. 753-763
  22. He, J.-H., Exp-Function Method for Fractional Differential Equations, International Journal of Nonline-ar Sciences and Numerical Simulation, 6 (2013), 14, pp. 363-366
  23. Jia, S. M., et al., Exact Solution of Fractional Nizhnik-Novikov-Veselov Equation, Thermal Science, 18 (2014), 5, pp. 1716-1717
  24. Ma, H. C., et al., Exact Solutions of Nonlinear Fractional Partial Differential Equations by Fractional Sub-Equation Method, Thermal Science, 19 (2015), 4, pp. 1239-1244
  25. Keskin, Y., Otutanc, G., The Reduced Differential Transform Method for Partial Differential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 6, pp. 741-749
  26. Keskin, Y., Otutanc, G., The Reduced Differential Transform Method for Solving Linear and Nonlinear Wave Equations, Iran. J. Sci. Technol, 34 (2010), 2, pp.113-122

© 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