THERMAL SCIENCE
International Scientific Journal
THE LOCAL FRACTIONAL ITERATION SOLUTION FOR THE DIFFUSION PROBLEM IN FRACTAL MEDIA
ABSTRACT
In this paper, we address the coupling method for the local fractional variational iteration algorithm III and local fractional Laplace transform for the first time, which is called as the local fractional Laplace transform variational iteration algorithm III. The proposed technology is used to find the local fractional iteration solution for the diffusion problem in fractal media via local fractional derivative.
KEYWORDS
PAPER SUBMITTED: 2015-12-10
PAPER REVISED: 2016-01-20
PAPER ACCEPTED: 2016-01-21
PUBLISHED ONLINE: 2016-09-24
THERMAL SCIENCE YEAR
2016, VOLUME
20, ISSUE
Supplement 3, PAGES [S743 - S746]
- Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
- Yang, X. J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
- He, J.-H., Local Fractional Variational Iteration Method for Fractal Heat Transfer in Silk Cocoon Hierarchy, Nonlinear Science Letters A, 4 (2013), 1, pp. 15-20
- Baleanu, D., et al., On the Exact Solution of Wave Equations on Cantor Sets, Entropy, 17 (2015), 9, pp. 6229-6237
- Yang, X. J., et al., Local Fractional Variational Iteration Method for Diffusion and Wave Equations on Cantor Sets, Romanian Journal of Physics, 59 (2014), 1-2, pp. 36-48
- Yang, A. M., et al., The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method, Advances in Mathematical Physics, 2014 (2014), ID 983254
- Zhang, Y., et al., An Efficient Analytical Method for Solving Local Fractional Nonlinear PDEs Arising in Mathematical Physics, Applied Mathematical Modelling, 40 (2016), 3, pp. 1793-1799
- Liu, C. F., et al., Reconstructive Schemes for Variational Iteration Method within Yang-Laplace Transform with Application to Fractal Heat Conduction Problem, Thermal Science, 17 (2013), 3, pp. 715-721
- Li, Y., et al., Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow, Advances in Mathematical Physics, 2014 (2014), ID 649318
- Jassim, H. K., et al., Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 (2015), ID 309870
- Goswami, P., et al., On the Solution of Local Fractional Differential Equations Using Local Fractional Laplace Variational Iteration Method, Mathematical Problems in Engineering, 2016 (2016), ID 9672314
- Yang, A. M., et al., Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative, Discrete Dynamics in Nature and Society, 2014 (2014), ID 365981
- Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
- Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84 (2015), 1, pp. 3-7
- 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
- Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
- 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, Communications in Nonlinear Science and Numerical Simulation, 29 (2015), 1, pp. 499-504
- Yang, X. J., et al., Local Fractional Variational Iteration Method and its Algorithms, Advances in Computational Mathematics and Applications, 1 (2012), 3, pp. 139-145
- Baleanu, D., et al., Local Fractional Variational Iteration Algorithms for the Parabolic Fokker-Planck Equation Defined on Cantor Sets, Prog. Fract. Differ. Appl., 1 (2015), 1, pp. 1-11
- Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250