Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets
Open Access
- 1 January 2013
- journal article
- research article
- Published by Wiley in Abstract and Applied Analysis
- Vol. 2013, 1-5
Abstract
We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.Keywords
Funding Information
- National Natural Science Foundation of China (11126213, 61170317)
- National Natural Science Foundation of China (11126213, 61170317)
This publication has 38 references indexed in Scilit:
- Fractal heat conduction problem solved by local fractional variation iteration methodThermal Science, 2013
- Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach–Adomian–Meyers modified decomposition methodApplied Mathematics and Computation, 2012
- Applications of Yang-Fourier Transform to Local Fractional Equations with Local Fractional Derivative and Local Fractional IntegralAdvanced Materials Research, 2012
- Heat-balance integral to fractional (half-time) heat diffusion sub-modelThermal Science, 2010
- Probability calculus of fractional order and fractional Taylor’s series application to Fokker–Planck equation and information of non-random functionsChaos, Solitons & Fractals, 2009
- Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equationCommunications in Nonlinear Science and Numerical Simulation, 2009
- Time–space fabric underlying anomalous diffusionChaos, Solitons & Fractals, 2006
- The elastic problem for fractal media: basic theory and finite element formulationComputers & Structures, 2003
- A fractional calculus approach to the description of stress and strain localization in fractal mediaChaos, Solitons & Fractals, 2002
- Local Fractional Fokker-Planck EquationPhysical Review Letters, 1998