Local fractional series expansion method for solving wave and diffusion equations on Cantor sets
type: Item
instance of: scholarly article
title: Local fractional series expansion method for solving wave and diffusion equations on Cantor sets
zbMATH Open document ID: 1295.35178
DOI: 10.1155/2013/351057
author: Aimin Yang
author: Xiao-Jun Yang
author: Zheng-Biao Li
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35L10
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6306679
zbMATH Keywords: efficiency and accuracy
Wikidata QID: Q58101440
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/351057
OpenAlex ID: W2125576051
cites work: Q5699297
cites work: Q5190149
cites work: Q4233638
cites work: Q5302855
cites work: Nonlinear and Complex Dynamics
cites work: The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations
cites work: Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach-Adomian-meyers modified decomposition method
cites work: Analytical solution of a fractional diffusion equation by variational iteration method
cites work: Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
cites work: Homotopy perturbation method for nonlinear partial differential equations of fractional order
cites work: Q3006513
cites work: Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
cites work: Fractional variational iteration method and its application
cites work: Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science
cites work: A fractional variational iteration method for solving fractional nonlinear differential equations
cites work: Fractional sub-equation method and its applications to nonlinear fractional PDEs
cites work: Fractional subequation method for Cahn-Hilliard and Klein-Gordon equations
cites work: Q4921007
cites work: Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator
cites work: One-phase problems for discontinuous heat transfer in fractal media
cites work: Local Fractional Fokker-Planck Equation
cites work: Diffusion problems in fractal media defined on Cantor sets
cites work: A fractional calculus approach to the description of stress and strain localization in fractal media
cites work: On calculus of local fractional derivatives
cites work: About non-differentiable functions
cites work: On the local fractional derivative
cites work: Time-space fabric underlying anomalous diffusion
cites work: Anomalous diffusion modeling by fractal and fractional derivatives
cites work: Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions
cites work: Laplace's transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative
cites work: Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method
cites work: Local fractional Fourier series with application to wave equation in fractal vibrating string
cites work: Advances in applied mathematics and approximation theory. Contributions from AMAT 2012 -- International conference on applied mathematics and approximation theory, Ankara, Turkey, May 17--20, 2012
cites work: Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives
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description: scientific article; zbMATH DE number 6306679