Fractional heat conduction models and thermal diffusivity determination
type: Item
instance of: scholarly article
title: Fractional heat conduction models and thermal diffusivity determination
zbMATH Open document ID: 1394.80010
DOI: 10.1155/2015/753936
author: Monika Žecová
author: Ján Terpák
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 6927159
Wikidata QID: Q59119810
describes a project that uses: ma2dfc
describes a project that uses: Heat Conduction Toolbox
describes a project that uses: Matlab
describes a project that uses: Fractional Heat Conduction Toolbox
describes a project that uses: mlrnd
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/753936
OpenAlex ID: W1486764886
cites work: CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
cites work: Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
cites work: Matrix approach to discrete fractional calculus. III: Non-equidistant grids, variable step length and distributed orders
cites work: Modelling heat transfer in heterogeneous media using fractional calculus
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: On the Appearance of the Fractional Derivative in the Behavior of Real Materials
cites work: Q4726489
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Some noises withI/fspectrum, a bridge between direct current and white noise
cites work: Q4844955
cites work: A universal circuit for studying chaotic phenomena
cites work: Fractional-order nonlinear systems. Modeling, analysis and simulation
cites work: Wright functions as scale-invariant solutions of the diffusion-wave equation
cites work: Solution for a fractional diffusion-wave equation defined in a bounded domain
cites work: Time fractional advection-dispersion equation
cites work: The fundamental solution of the space-time fractional diffusion equation
cites work: The time fractional diffusion equation and the advection-dispersion equation
cites work: The fractional diffusion equation
cites work: Fractional diffusion and wave equations
cites work: Time- and space-fractional partial differential equations
cites work: Time fractional diffusion: A discrete random walk approach
cites work: Fully discrete random walks for space-time fractional diffusion equations
cites work: Q5708108
cites work: Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method
cites work: Q5708139
cites work: Implicit difference approximation for the time fractional diffusion equation
cites work: A second-order accurate numerical method for the two-dimensional fractional diffusion equation
cites work: Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in \(\mathbb R^2\)
cites work: Least squares finite-element solution of a fractional order two-point boundary value problem
cites work: Variational formulation for the stationary fractional advection dispersion equation
cites work: Variational solution of fractional advection dispersion equations on bounded domains in ℝd
cites work: An approximate method for numerical solution of fractional differential equations
cites work: A numerical scheme for initial compliance and creep response of a system
cites work: Numerical solutions of the space-time fractional advection-dispersion equation
cites work: Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition
cites work: Monte Carlo evaluation of FADE approach to anomalous kinetics
cites work: Q4438509
cites work: A restarted Lanczos approximation to functions of a symmetric matrix
cites work: Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
cites work: An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
cites work: Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
cites work: Finite difference approximations for the fractional Fokker-Planck equation
cites work: The accuracy and stability of an implicit solution method for the fractional diffusion equation
cites work: A second-order accurate numerical approximation for the fractional diffusion equation
cites work: Numerical approximations for fractional diffusion equations via splines
cites work: Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
cites work: Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
description: scientific article; zbMATH DE number 6927159