Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics
type: Item
instance of: scholarly article
title: Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics
zbMATH Open document ID: 1109.26005
author: Mingyu Xu
author: Wenchang Tan
published in: Science in China. Series G
publication date: 2006-10-11T00:00:00Z
review text: The authors present a detailed survey of application of fractional operators (with emphasis on fractional differential equation) used for describing intermediate processes and critical phenomena in physics and mechanics. In particular the application of FO in various complex systems, e.g. dynamical problems of linear and nonlinear fluid mechanics, biophysics, biomechanics, theory of random walk and anomalous diffusion, research of DLA (diffusion limited aggregation) theory, has been included. At the end prospects and evaluation for this subject are made.
reviewed by: Mridula Garg
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 5062431
MaRDI profile type: Publication
full work available at URL: s11433-006-0257-2
OpenAlex ID: W2156507970
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Q3141895
cites work: Q3141902
cites work: Q4740120
cites work: Fractional calculus and its applications. Proceedings of the international conference held at the University of New Haven, June 1974
cites work: An introduction to fractional calculus
cites work: Applications of fractional calculus in physics
cites work: Fractional Brownian Motions, Fractional Noises and Applications
cites work: Q4154814
cites work: Q4524288
cites work: Q4543045
cites work: Fractals, scaling and growth far from equilibrium
cites work: Q4520870
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Applications of fractional calculus techniques to problems in biophysics
cites work: Applications to problems in polymer physics and rheology.
cites work: ON THE RIEMANN-LIOUVILLE FRACTIONAL CALCULUS AND SOME RECENT APPLICATIONS
cites work: Generalized viscoelastic models: their fractional equations with solutions
cites work: Fox function representation of non-Debye relaxation processes
cites work: Fractional calculus and regular variation in thermodynamics.
cites work: Fractional calculus and some intermediate physical processes.
cites work: Q3122730
cites work: Q4484084
cites work: Analysis of nonlinear vibrations of a two-degree-of-freedom mechanical system with damping modelled by a fractional derivative
cites work: Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems
cites work: Q4161583
cites work: Q4743083
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: Wright functions as scale-invariant solutions of the diffusion-wave equation
cites work: Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion.
cites work: A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates
cites work: The impulsive motion of flat plate in a generalized second-grade fluid.
cites work: Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe
cites work: Analysis of general second-order fluid flow in double cylinder rheometer
cites work: Fractal dynamics in the growth of root
cites work: An analytical solution for the model of drug distribution and absorption in small intestine
cites work: MINIMUM ENERGY DISSIPATION AND FRACTAL STRUCTURES OF VASCULAR SYSTEMS
cites work: An exact solution to the moving boundary problem with fractional anomalous diffusion in drug release devices
cites work: Q4421708
cites work: Q4229072
cites work: Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
cites work: Fractals and fractional calculus in continuum mechanics
cites work: Fractional diffusion equation on fractals: three-dimensional case and scattering function
cites work: Concentration distribution of fractional anomalous diffusion caused by an instantaneous point source
cites work: Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations
cites work: The explicit solutions of a class of diffusion equation
cites work: Q4873703
cites work: Formulation of Euler-Lagrange equations for fractional variational problems
cites work: Dynamics of the fractional oscillator
cites work: Fractional quantum mechanics and Lévy path integrals
cites work: Fractals and quantum mechanics.
cites work: Time fractional Schrödinger equation
cites work: The scaled universe
cites work: Mittag-Leffler coherent states
cites work: Quantization of the anomalous Brownian motion
cites work: Fractional differential forms
cites work: Fractional operators and special functions. I. Bessel functions
cites work: Fractional operators and special functions. II. Legendre functions
cites work: A fractional calculus approach to the description of stress and strain localization in fractal media
cites work: The relationship of fractals in geophysics to ``the new science''
cites work: THE DYNAMICS OF FRACTALS
cites work: Viscous fingering in non-Newtonian fluids
cites work: Q3150942
cites work: Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models
DOI: 10.1007/S11433-006-0257-2