## THERMAL SCIENCE

International Scientific Journal

### A NEW COMPUTATIONAL METHOD FOR THE ONE-DIMENSIONAL DIFFUSION PROBLEM WITH THE DIFFUSIVE PARAMETER VARIABLE IN FRACTAL MEDIA

**ABSTRACT**

In this paper, we use a local fractional Laplace decomposition method to solve the diffusion equation with the diffusive parameter variable in fractal media. The obtained result illustrates the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

**KEYWORDS**

PAPER SUBMITTED: 2014-10-10

PAPER REVISED: 2015-01-22

PAPER ACCEPTED: 2015-02-12

PUBLISHED ONLINE: 2015-08-02

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**Supplement 1**, PAGES [S117 - S122]

- Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science, New York, USA, 2012
- Yang, X. J., Local Fractional Integral Transforms, Progress in Nonlinear Science, 4(2011), 1, pp. 1-225
- Yang, X. J., Local Fractional Functional Analysis & Its Applications, Asian Academic Publisher, Hong Kong, 2011
- Zhao, Y., et al., Maxwell’s Equations on Cantor Sets: a Local Fractional Approach, Advances in High Energy Physics, 2013 (2013), ID 686371
- Kolwankar, K. M., Gangal, A. D., Local Fractional Fokker-Planck Equation, Physical Review Letters, 80(1998), 2, pp. 2-14
- Yang, X. J., et al., Mathematical Aspects of the Heisenberg Uncertainty Principle within Local Fractional Fourier Analysis, Boundary Value Problems, 2013(2013), 1, May, pp. 1-16
- Yang, X. J., et al., Cantor-Type Cylindrical-Coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letters A, 377(2013), 28, pp. 1696-1700
- Carpinteri, A., Cornetti, P., A Fractional Calculus Approach to the Description of Stress and Strain Localization in Fractal Media, Chaos, Solitons & Fractals, 13 (2002), 1, pp. 85-94
- Zhang, Y., et al., On a Local Fractional Wave Equation under Fixed Entropy Arising in Fractal Hydrodynamics, Entropy, 16(2014), 12, pp. 6254-6262
- Carpinteri, A., et al., Static-Kinematic Duality and the Principle of Virtual Work in the Mechanics of Fractal Media, Computer Methods in Applied Mechanics and Engineering, 191(2001), 1, pp. 3-19
- Yang, X. J., et al., Systems of Navier-Stokes Equations on Cantor Sets, Mathematical Problems in Engineering, 2013 (2013), ID 769724
- Carpinteri, A., et al. , On the Mechanics of Quasi-Brittle Materials with a Fractal Microstructure, Engineering Fracture Mechanics, 70(2003), 16, pp. 2321-2349
- Yang, X. J., et al., On Local Fractional Continuous Wavelet Transform, Abstract and Applied Analysis, 2013(2013), ID 725416
- Zhao, Y. et al., Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets, Mathematical Problems in Engineering, 2013(2013), ID 560932
- Chen, Z. Y., et al., Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach, Advances in Mathematical Physics, 2014(2014), ID 561434
- Yan, S. P., et al., Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014(2014), ID 161580
- Cao, Y., et al., Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets, Abstract and Applied Analysis 2014(2014), ID 803693
- Wang, S. Q. et al., Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014 (2014), ID 176395
- 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, in press
- 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
- 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
- Baleanu, D., et al., Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators, Abstract and Applied Analysis, 2014 (2014), ID 535048
- 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, 461(2012), 2, pp.306-310
- Yang, A. M., et al., The Yang-Fourier Transforms to Heat-Conduction in a Semi-Infinite Fractal Bar, Thermal Science, 17(2013), 3, pp. 707-713
- Zhang, Y. Z., et al., Initial Boundary Value Problem for Fractal Heat Equation in the Semi-Infinite Region by Yang-Laplace Transform, Thermal Science, 18 (2014), 2, pp. 677-681
- Zhao, C. G., et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis 2014 (2014), ID 386459
- 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
- Cattani, C., et al., Fractional Dynamics, Emerging science publishers, 2015
- Srivastava, H. M., et al., Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), ID 620529