Renormalization group and fractional calculus methods in a complex world: a review
From MaRDI portal
Publication:2020222
DOI10.1515/fca-2021-0002zbMath1488.81034OpenAlexW3133807861MaRDI QIDQ2020222
Bruce J. West, Lihong Guo, Shaoyun Shi, Yang Quan Chen
Publication date: 23 April 2021
Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/fca-2021-0002
Fractional processes, including fractional Brownian motion (60G22) Singular perturbations in context of PDEs (35B25) Fractional derivatives and integrals (26A33) Renormalization group methods applied to problems in quantum field theory (81T17) Renormalization group methods in equilibrium statistical mechanics (82B28) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singular perturbations of functional-differential equations (34K26) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Comparative study of homotopy analysis and renormalization group methods on Rayleigh and Van der Pol equations
- Generalized central limit theorem and renormalization group
- On the renormalization group approach to perturbation theory for PDEs
- Renormalization group method applied to the primitive equations
- Experimental critical-exponent values for fluids
- Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations
- Fractal random walks
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- On the solutions of the renormalized equations at all orders.
- Renormalization group method. Application to Navier-Stokes equation
- On the average uncertainty for systems with nonlinear coupling
- Singular perturbed renormalization group theory and its application to highly oscillatory problems
- The renormalization method based on the Taylor expansion and applications for asymptotic analysis
- Renormalization group approach to power-law modeling of complex metabolic networks
- A new metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces
- Stochastic Navier-Stokes equation and renormalization group theory
- The Pareto law of incomes - an explanation and an extension
- Comments on the renormalization group, scaling and measures of complexity
- Renormalization group derivation of phase equations
- Renormalization-group method for reduction of evolution equations; invariant manifolds and envelopes.
- Renormalization group approach to boundary layer problems
- A new collection of real world applications of fractional calculus in science and engineering
- Multiple existence of indefinite nonlinear diffusion problem in population genetics
- Continuous time random walk models associated with distributed order diffusion equations
- Fractional calculus in image processing: a review
- Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion
- First and second order approximations for a nonlinear wave equation
- Singular perturbation systems with stochastic forcing and the renormalization group method
- An analysis of the renormalization group method for asymptotic expansions with logarithmic switchback terms
- Critical phenomena in natural sciences. Chaos, fractals, selforganization and disorder: Concepts and tools.
- The flow equation approach to many-particle systems
- Small distance behaviour in field theory and power counting
- On a certain renormalization group method
- Phase Transition and Fractals
- The Renormalization Group: A Perturbation Method for the Graduate Curriculum
- First order approximation for quadratic dispersive equations by the renormalization group approach
- Ultra-short pulses in linear and nonlinear media
- Renormalization group theory: Its basis and formulation in statistical physics
- Preface to the second edition
- Stable and Random Motions in Dynamical Systems
- Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method
- Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
- Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
- Introduction to Nonextensive Statistical Mechanics
- $C^1$ Approximation of Vector Fields Based on the Renormalization Group Method
- The Use of an lnvariance Condition in the Solution of Multiple‐Scale Singular Perturbation Problems: Ordinary Differential Equations
- Flow‐equations for Hamiltonians
- Renormalization Group Theory for Global Asymptotic Analysis
- Renormalization group theory of anomalous transport in systems with Hamiltonian chaos
- Statistical mechanics for complex systems: On the structure of q-triplets
- Renormalization group second‐order approximation for singularly perturbed nonlinear ordinary differential equations
- A New Renormalization Method for the Asymptotic Solution of Weakly Nonlinear Vector Systems
- A Uniformly‐Valid Asymptotic Solution to a Matrix System of Ordinary Differential Equations and a Proof of its Validity
- Fractional dynamics of allometry
- Nature’s Patterns and the Fractional Calculus
- Reviews of Nonlinear Dynamics and Complexity
- SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
- Fractional Brownian Motions, Fractional Noises and Applications
- Expected Number of Distinct Sites Visited by a Random Walk with an Infinite Variance
- Quantum Electrodynamics at Small Distances
- An elementary renormalization-group approach to the generalized central limit theorem and extreme value distributions
- The spectral dimension of simplicial complexes: a renormalization group theory
- Information and self-organization. A macroscopic approach to complex systems.
- Renormalization group method. Applications to partial differential equations
- Renormalization group and probability theory
This page was built for publication: Renormalization group and fractional calculus methods in a complex world: a review
