THERMAL SCIENCE
International Scientific Journal
A MODIFICATION OF THE REDUCED DIFFERENTIAL TRANSFORM METHOD FOR FRACTIONAL CALCULUS
ABSTRACT
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.
KEYWORDS
PAPER SUBMITTED: 2016-12-03
PAPER REVISED: 2017-10-20
PAPER ACCEPTED: 2017-12-08
PUBLISHED ONLINE: 2018-09-10
THERMAL SCIENCE YEAR
2018, VOLUME
22, ISSUE
Issue 4, PAGES [1871 - 1875]
- 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
- Kumar, S., A New Fractional Modeling Arising in Engineering Sciences and Its Analytical Approximate Solution, Alexandria Engineering Journal, 52 (2013), 4, pp. 813-819
- 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
- 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
- Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
- 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
- He, J.-H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, Int. J. Theor. Phys, 53 (2014), 11, pp. 3698-3718
- Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
- Zhao, D. Z., Luo, M. K., General Conformable Fractional Derivative and Its Physical Interpretation, Calcolo, 54 (2017), 3, pp. 903-917
- Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of Mathemati-cal Analysis and Applications, 135 (1988), 2, pp. 501-544
- He, J.-H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Applied Mathemat-ics and Computation, 135 (2003), 1, pp. 73-79
- 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
- He, J.-H., Application of Homotopy Perturbation Method to Nonlinear Wave Equation, Chaos, Solitons & Fractals, 26 (2005), 3, pp. 695-700
- Rajeev., Homotopy Perturbation Method for a Stefan Problem with Variable Latent Heat, Thermal Sci-ence, 18 (2014), 2, pp. 391-398
- 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
- 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
- He, J.-H., Variational Iteration Method - Some Recent Results and New Interpretations, J. Comput. Appl. Math., 207 (2007), 1, pp. 3-17
- Lin, J., Lu, J. F., Variational Iteration Method for the Classical D-Sokolov-Wilson Equation, Thermal Science, 18 (2014), 5, pp. 1543-1546
- 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
- 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
- Daftardar, G., Hossein, J., An Iterative Method for Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications, 316 (2006), 2, pp. 753-763
- 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
- Jia, S. M., et al., Exact Solution of Fractional Nizhnik-Novikov-Veselov Equation, Thermal Science, 18 (2014), 5, pp. 1716-1717
- 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
- 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
- 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