THERMAL SCIENCE

International Scientific Journal

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LOCAL FRACTIONAL HELMHOLTZ SIMULATION FOR HEAT CONDUCTION IN FRACTAL MEDIA

ABSTRACT
In this paper, we consider the generalized local fractional 2-D Helmholtz equation in steady heat transfer process, which can be used to model the steady-state heat conduction in fractal media. The Yang-Fourier transform and Yang-Laplace transform method are used to solve the equation. The integral expression of the solutions is obtained in detail.
KEYWORDS
PAPER SUBMITTED: 2018-03-12
PAPER REVISED: 2018-06-18
PAPER ACCEPTED: 2018-11-23
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180312238D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 3, PAGES [1671 - 1675]
REFERENCES
1. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, NY, USA, 2012
2. Momani, S., et al., Application of He's Variational Iteration Method to Helmholtz Equation, Chaos Solitons and Fractals, 5(2006), 27, pp.1119-1123
3. Rafei, M., et al., Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method, International Journal of Nonlinear Sciences and Numerical Simulation, 3(2006), 7, pp.321-328
4. Yang, X. J., et al., On Exact Traveling-wave Solutions for Local Fractional KdV Equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(2016), 8, Article ID 084312, pp.1-8
5. Yang, X. J., et al., Local Fractional Similarity Solution for The Diffusion Equation Defined On Cantor Sets. Applied Mathematics Letters, 47(2015), 1, pp.54-60
6. 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), pp.752-761
7. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), Sep., pp.285-296
8. Yang, X. J., et al., Exact Traveling-wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25(2017), 4, pp.1-6
9. Choi, J., et al., Certain Generalized Ostrowski Type Inequalities for Local Fractional Integrals. Communications of the Korean Mathematical Society, 32(2017), 3, pp. 617-624
10. Sun, W., On Generalization of Some Inequalities for Generalized Harmonically Convex Functions via Local Fractional Integrals. Quaestiones Mathematicae, 2018, pp.1-25
11. Anastassiou, G., et al., Local Fractional Integrals Involving Generalized Strongly M-Convex Mappings. Arabian Journal of Mathematics, 2018, 1, pp.1-13
12. Jafari, H., et al., Local Fractional Series Expansion Method for Solving Laplace and Schrodinger Equations on Cantor Sets within Local Fractional Operators, International Journal of Mathematics and Computer Research,11(2014), 2, pp.736-744
13. 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
14. Sahoo, S., et al., New Solitary Wave Solutions of Time-Fractional Coupled Jaulent-Miodek Equation by Using Two Reliable Methods. Nonlinear Dynamics, 85(2016), 2, pp.1167-1176
15. Kumar, D., et al., A Hybrid Computational Approach for Klein-Gordon Equations on Cantor Sets. Nonlinear Dynamics, 87(2017), 1, pp.511-517
16. Baleanu, D., et al., Local Fractional Variational Iteration and Decomposition Methods for Wave Equation On Cantor Sets, Abstract and Applied Analysis, Article ID 535048(2014), pp.1-6
17. Yang, X. J., et al., A New Family of the Local Fractional PDEs, Fundamenta Informaticae, 2017, 151(1-4), pp. 63-75
18. Yang, X. J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 2017, 69(3), 113
19. Yang, X. J., et al., Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-De Vries Equation, Abstract and Applied Analysis, 2014,Aricle ID 278672
20. Ahmad, J., et al., Analytic Solutions of the Helmholtz and Laplace Equations by Using Local Fractional Derivative Operators, Waves Wavelets and Fractals, 1(2015), 1, pp.22-26
21. Hao, Y. J., et al., Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates, Advances in Mathematical Physics, 754248(2013), 2013, pp.1-5
22. Yang, A. M., et al., Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators, Abstract and Applied Analysis, Article ID 259125(2013), pp.1-6
23. Zhao, C. G., et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis, 6(2014), 2014, pp.1-5
24. Zhong, W. P., et al., Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional Integral, Advanced Materials Research, 46(2012), 1, pp.306-310