Local fractional Fourier series with application to wave equation in fractal vibrating string
type: Item
instance of: scholarly article
title: Local fractional Fourier series with application to wave equation in fractal vibrating string
zbMATH Open document ID: 1257.35193
DOI: 10.1155/2012/567401
author: Ming-Sheng Hu
author: Ravi P. Agarwal
author: Xiao-Jun Yang
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 33E12
Mathematics Subject Classification ID: 81Q35
zbMATH DE Number: 6134113
Wikidata QID: Q58101549
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/567401
OpenAlex ID: W2095733540
cites work: Advances in Fractional Calculus
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Q3141902
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q3141895
cites work: Q5699297
cites work: Fractional diffusion and wave equations
cites work: Solution for a fractional diffusion-wave equation defined in a bounded domain
cites work: Fractional-order diffusion-wave equation
cites work: Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
cites work: Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder
cites work: The Wright functions as solutions of the time-fractional diffusion equation.
cites work: Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
cites work: Stochastic solution of space-time fractional diffusion equations
cites work: Cauchy problem for fractional diffusion equations
cites work: The general time fractional wave equation for a vibrating string
cites work: Generalized wave equation in nonlocal elasticity
cites work: Space-time fractional Schrödinger equation with time-independent potentials
cites work: On the solution of the fractional nonlinear Schrödinger equation
cites work: Numerical treatment of fractional heat equations
cites work: An explicit and numerical solutions of the fractional KdV equation
cites work: The fractional Fick's law for non-local transport processes
cites work: Nonlocal Cauchy problem for fractional evolution equations
cites work: Fractional Heisenberg equation
cites work: Fractional hydrodynamic equations for fractal media
cites work: Approximate analytical solution for seepage flow with fractional derivatives in porous media
cites work: Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method
cites work: Fractional variational iteration method and its application
cites work: A short remark on fractional variational iteration method
cites work: Fractional complex transform for fractional differential equations
cites work: Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus
cites work: On the representation of fractional Brownian motion as an integral with respect to \((dt)^a\)
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: Adomian decomposition method for non-smooth initial value problems
cites work: Local Fractional Fokker-Planck Equation
cites work: Diffusion problems in fractal media defined on Cantor sets
cites work: Fractional differentiability of nowhere differentiable functions and dimensions
cites work: On calculus of local fractional derivatives
cites work: CALCULUS ON FRACTAL SUBSETS OF REAL LINE — I: FORMULATION
cites work: About non-differentiable functions
cites work: A disordered microstructure material model based on fractal geometry and fractional calculus
cites work: A fractional calculus approach to the description of stress and strain localization in fractal media
cites work: On the local fractional derivative
cites work: Fractional sub-equation method and its applications to nonlinear fractional PDEs
cites work: Asymptotic methods for solitary solutions and compactons
description: scientific article; zbMATH DE number 6134113