THERMAL SCIENCE
International Scientific Journal
A NOVEL SCHEDULE FOR SOLVING THE TWO-DIMENSIONAL DIFFUSION PROBLEM IN FRACTAL HEAT TRANSFER
ABSTRACT
In this work, the local fractional variational iteration method is employed to obtain approximate analytical solution of the two-dimensional diffusion equation in fractal heat transfer with help of local fractional derivative and integral operators.
KEYWORDS
PAPER SUBMITTED: 2014-11-15
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 [S99 - S103]
- Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science, New York, USA, 2012
- 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, 2013 (2013), ID 754248
- Yang, X. J., et al., Mathematical Aspects of the Heisenberg Uncertainty Principle within Local Fractional Fourier Analysis, Boundary Value Problems, 2013 (2013), 1, pp. 1-16
- Yang, X.-J., et al., Modeling Fractal Waves on Shallow Water Surfaces via Local Fractional Kortewegde Vries Equation, Abstract and Applied Analysis, 2014 (2014), ID 278672
- Yang, X. J., et al., Approximate Solutions for Diffusion Equations on Cantor Space-Time, Proceedings of the Romanian Academy, Series A, 14 (2013), 2, pp. 127-133
- Yang, A. M., et al., Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets, Abstract and Applied Analysis, 2013 (2013), ID 351057
- 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
- Cao, Y., et al., Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), ID 803693
- Yang, X. J., Baleanu, D., 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
- Su, W. H. et al., Damped Wave Equation and Dissipative Wave Equation in Fractal Strings within the Local Fractional Variational Iteration Method, Fixed Point Theory and Applications, 2013 (2013), 1, pp. 89-102
- Yang, Y. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 (2013), ID 202650
- 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
- Baleanu, D., et al., Local Fractional Variational Iteration Algorithms for the Parabolic Fokker-Planck Equation Defined on Cantor Sets, Progress in Fractional Differentiation and Applications, 1 (2015), 1, pp. 1-11
- Neamah, A. A., Local Fractional Variational Iteration Method for Solving Volterra Integro-Differential Equations with Local Fractional Operators, Journal of Mathematics and Statistics, 10 (2014), 3, pp. 401-407
- He, J.-H., A Tutorial Review on Fractal Space-Time and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718