Fractional diffusion in inhomogeneous media
From MaRDI portal
Publication:5706146
DOI10.1088/0305-4470/38/42/L03zbMath1082.76097OpenAlexW1971359112MaRDI QIDQ5706146
Rudolf Gorenflo, Aleksei V. Chechkin, Igor M. Sokolov
Publication date: 4 November 2005
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0305-4470/38/42/l03
Related Items (only showing first 100 items - show all)
A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana-Baleanu-Caputo derivative ⋮ Subdiffusion equations with a source term and their extensions ⋮ Anomalous diffusion in nonhomogeneous media: power spectral density of signals generated by time-subordinated nonlinear Langevin equations ⋮ Structure and transport properties of ethylcellulose membranes with different types and granulation of magnetic powder ⋮ Existence and uniqueness of an inverse source problem for a fractional integrodifferential equation ⋮ Optimal control problem of variable-order delay system of advertising procedure: numerical treatment ⋮ Two-dimensional Legendre wavelets for solving variable-order fractional nonlinear advection-diffusion equation with variable coefficients ⋮ General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems ⋮ On semi-Markov processes and their Kolmogorov's integro-differential equations ⋮ A fast collocation method for solving the weakly singular fractional integro-differential equation ⋮ Exponential-sum-approximation technique for variable-order time-fractional diffusion equations ⋮ The analytical interface coupling of arbitrary-order fractional nonlinear hyperbolic scalar conservation laws ⋮ Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework ⋮ Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions ⋮ Conformable derivative approach to anomalous diffusion ⋮ Variable order fractional Fokker-Planck equations derived from continuous time random walks ⋮ Time-fractional differential equations with variable order using RDTM and ADM: application to infectious-disease model ⋮ Method of approximate particular solutions for constant- and variable-order fractional diffusion models ⋮ An extension of the singular boundary method for solving two dimensional time fractional diffusion equations ⋮ Continuous time random walk with \(A \rightarrow B\) reaction in flows ⋮ Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain ⋮ Data regularization for a backward time-fractional diffusion problem ⋮ Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order ⋮ Legendre wavelets optimization method for variable-order fractional Poisson equation ⋮ A note on fractional order derivatives and table of fractional derivatives of some special functions ⋮ A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of noninteger derivatives ⋮ The stretch to stray on time: Resonant length of random walks in a transient ⋮ Variable-order fractional mean square displacement function with evolution of diffusibility ⋮ Fractional Feynman-Kac equation with space-dependent anomalous exponent ⋮ Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation ⋮ A review of applications of fractional calculus in Earth system dynamics ⋮ Random-order fractional differential equation models ⋮ Transport equations for subdiffusion with nonlinear particle interaction ⋮ Identification of a kernel in an evolutionary integral equation occurring in subdiffusion ⋮ Semi-Markov models and motion in heterogeneous media ⋮ A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation ⋮ A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations ⋮ An optimization method based on the generalized polynomials for nonlinear variable-order time fractional diffusion-wave equation ⋮ Stability and regularity in inverse source problem for generalized subdiffusion equation perturbed by locally Lipschitz sources ⋮ Caputo derivatives of fractional variable order: numerical approximations ⋮ A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient ⋮ Reconstruction of an order of derivative and a source term in a fractional diffusion equation from final measurements ⋮ On Uncertain-Fractional Modeling: The Future Way of Modeling Real-World Problems ⋮ Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system ⋮ Weak solvability of the variable-order subdiffusion equation ⋮ Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation ⋮ Monitoring Lévy-process crossovers ⋮ A new semi-analytical method for solving a class of time fractional partial differential equations with variable coefficients ⋮ A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation ⋮ On the generalized mass transport equation to the concept of variable fractional derivative ⋮ Local fractional \(Z\)-transforms with applications to signals on Cantor sets ⋮ Some further generalizations of Hölder's inequality and related results on fractal space ⋮ A computational wavelet method for variable-order fractional model of dual phase lag bioheat equation ⋮ STOCHASTIC RESONANCE OF NON-MARKOVIAN RENEWAL PROCESSES ⋮ A second-order numerical method for space-time variable-order diffusion equation ⋮ Topological states in the Hofstadter model on a honeycomb lattice ⋮ Continuity of solutions of a class of fractional equations ⋮ On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation ⋮ Continuous-time random walks in an oscillating field: Field-induced dispersion and the death of linear response ⋮ A full-stage creep model for rocks based on the variable-order fractional calculus ⋮ A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives ⋮ FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION ⋮ Fast algorithms for high-dimensional variable-order space-time fractional diffusion equations ⋮ An operational matrix method for solving variable-order fractional biharmonic equation ⋮ Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates ⋮ A new approach of superconvergence analysis for two-dimensional time fractional diffusion equation ⋮ A wavelet method to solve nonlinear variable-order time fractional 2D Klein-Gordon equation ⋮ A compact finite difference scheme for variable order subdiffusion equation ⋮ A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation ⋮ Analysis of local discontinuous Galerkin method for time-space fractional sine-Gordon equations ⋮ On using random walks to solve the space-fractional advection-dispersion equations ⋮ Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation ⋮ Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers ⋮ Uniqueness in inverse boundary value problems for fractional diffusion equations ⋮ Numerical solutions of variable order time fractional \((1+1)\)- and \((1+2)\)-dimensional advection dispersion and diffusion models ⋮ The effect of the junction model on the anomalous diffusion in the 3D comb structure ⋮ Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation ⋮ A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients ⋮ Maximum principle for the generalized time-fractional diffusion equation ⋮ The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation ⋮ Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation ⋮ Variable-order fractional calculus: a change of perspective ⋮ Matrix approach to discrete fractional calculus. II: Partial fractional differential equations ⋮ Explicit solutions of initial value problems for systems of linear Riemann-Liouville fractional differential equations with constant delay ⋮ On mean square displacement behaviors of anomalous diffusions with variable and random orders ⋮ Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits ⋮ Anomalous Diffusion: Models, Their Analysis, and Interpretation ⋮ Reliable methods to study some nonlinear conformable systems in shallow water ⋮ The arbitrary-order fractional hyperbolic nonlinear scalar conservation law ⋮ A parallel algorithm for space-time-fractional partial differential equations ⋮ Time-space variable-order fractional nonlinear system of thermoelasticity: numerical treatment ⋮ A non-integer variable order mathematical model of human immunodeficiency virus and malaria coinfection with time delay ⋮ Gegenbauer wavelet operational matrix method for solving variable-order non-linear reaction-diffusion and Galilei invariant advection-diffusion equations ⋮ Boundary functions determination in an inverse time fractional heat conduction problem ⋮ A direct method based on the Chebyshev polynomials for a new class of nonlinear variable-order fractional 2D optimal control problems ⋮ A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications ⋮ Maximum principle and its application for the time-fractional diffusion equations ⋮ A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures ⋮ Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density ⋮ Variable-order approach to nonlocal elasticity: theoretical formulation, order identification via deep learning, and applications
This page was built for publication: Fractional diffusion in inhomogeneous media