Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
From MaRDI portal
Publication:356343
DOI10.1016/j.camwa.2012.02.042zbMath1268.35124OpenAlexW1986713454MaRDI QIDQ356343
Publication date: 25 July 2013
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2012.02.042
analytical solutionmulti-term time-fractional diffusion equationsmulti-term time-fractional diffusion-wave equationsmultivariate Mittag-Leffler functionnonhomogeneous initial-boundary-value problemsseparating of variables
Related Items
A wavelet approach for the multi-term time fractional diffusion-wave equation ⋮ Gauss-Lobatto-Legendre-Birkhoff pseudospectral scheme for the time fractional reaction–diffusion equation with Neumann boundary conditions ⋮ Spatial high accuracy analysis of FEM for two-dimensional multi-term time-fractional diffusion-wave equations ⋮ First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval ⋮ Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations ⋮ Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker-Planck equation ⋮ Controllability of multi-term time-fractional differential systems with state-dependent delay ⋮ A stable fast time-stepping method for fractional integral and derivative operators ⋮ General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems ⋮ Analytical solutions for the fractional nonlinear cable equation using a modified homotopy perturbation and separation of variables methods ⋮ A block-centered finite difference method for the distributed-order time-fractional diffusion-wave equation ⋮ The asymptotics of the solutions to the anomalous diffusion equations ⋮ Analysis of a meshless method for the time fractional diffusion-wave equation ⋮ Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: meshless interpolating element free Galerkin (IEFG) and finite element methods ⋮ A new efficient algorithm based on fifth-kind Chebyshev polynomials for solving multi-term variable-order time-fractional diffusion-wave equation ⋮ An efficient hybrid numerical method for multi-term time fractional partial differential equations in fluid mechanics with convergence and error analysis ⋮ Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain ⋮ A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations ⋮ A Numerical-Analytical Method for Time-Fractional Dual-Phase-Lag Models of Heat Transfer ⋮ Numerical solution of time fractional diffusion systems ⋮ Compatibility of the Paraskevopoulos's algorithm with operational matrices of Vieta-Lucas polynomials and applications ⋮ Computational challenge of fractional differential equations and the potential solutions: a survey ⋮ A piecewise memory principle for fractional derivatives ⋮ Numerical algorithm with high spatial accuracy for the fractional diffusion-wave equation with von Neumann boundary conditions ⋮ Numerical methods for the two-dimensional multi-term time-fractional diffusion equations ⋮ A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain ⋮ Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation ⋮ Inversion of the initial value for a time-fractional diffusion-wave equation by boundary data ⋮ Novel analytical and numerical techniques for fractional temporal SEIR measles model ⋮ A compact exponential difference method for multi-term time-fractional convection-reaction-diffusion problems with non-smooth solutions ⋮ The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations ⋮ On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations ⋮ Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data ⋮ Uniqueness and stability for inverse source problem for fractional diffusion-wave equations ⋮ A <scp>kernel‐based pseudo‐spectral</scp> method for <scp>multi‐term</scp> and distributed order <scp>time‐fractional</scp> diffusion equations ⋮ Simultaneous inversion of two initial values for a time‐fractional diffusion‐wave equation ⋮ A fully spectral tau method for a class of linear and nonlinear variable-order time-fractional partial differential equations in multi-dimensions ⋮ Two-grid algorithms based on FEM for nonlinear time-fractional wave equations with variable coefficient ⋮ On Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equation ⋮ Solving time-fractional reaction-diffusion systems through a tensor-based parallel algorithm ⋮ The quasi-reversibility regularization method for backward problem of the multi-term time-space fractional diffusion equation ⋮ Modified fractional reduced differential transform method for the solution of multiterm time-fractional diffusion equations ⋮ Superconvergence analysis of anisotropic finite element method for the time fractional substantial diffusion equation with smooth and nonsmooth solutions ⋮ Approximate solution of the multi-term time fractional diffusion and diffusion-wave equations ⋮ Some novel numerical techniques for an inverse problem of the multi-term time fractional partial differential equation ⋮ On a non-local problem for a multi-term fractional diffusion-wave equation ⋮ Unnamed Item ⋮ Numerical Solutions and Pattern Formation Process in Fractional Diffusion-Like Equations ⋮ Determination of the initial data in a time-fractional diffusion-wave problem by a final time data ⋮ A novel finite volume method for the Riesz space distributed-order diffusion equation ⋮ Perturbation properties of fractional strongly continuous cosine and sine family operators ⋮ Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains ⋮ Reconstruction of the source term in a time-fractional diffusion equation from partial domain measurement ⋮ Method of separation variables combined with homogenous balanced principle for searching exact solutions of nonlinear time-fractional biological population model ⋮ A new semi-analytical method for solving a class of time fractional partial differential equations with variable coefficients ⋮ Finite difference scheme for simulating a generalized two-dimensional multi-term time fractional non-Newtonian fluid model ⋮ Transmutations for Multi-Term Fractional Operators ⋮ Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations ⋮ Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes ⋮ Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications ⋮ Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations ⋮ Simultaneous inversion for the diffusion and source coefficients in the multi-term TFDE ⋮ Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation ⋮ Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method ⋮ Separation variable method combined with integral bifurcation method for solving time-fractional reaction-diffusion models ⋮ An inverse source problem of space-fractional diffusion equation ⋮ Exact controllability of multi-term time-fractional differential system with sequencing techniques ⋮ Numerical Inversion for the Initial Distribution in the Multi-Term Time-Fractional Diffusion Equation Using Final Observations ⋮ Subordination approach to multi-term time-fractional diffusion-wave equations ⋮ Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients ⋮ A meshless point collocation method for 2-D multi-term time fractional diffusion-wave equation ⋮ New collocation scheme for solving fractional partial differential equations ⋮ Nonexistence of global solutions for a class of nonlocal in time and space nonlinear evolution equations ⋮ A space-time spectral collocation method for the two-dimensional variable-order fractional percolation equations ⋮ The backward problem for a time-fractional diffusion-wave equation in a bounded domain ⋮ Alternating direction implicit difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel ⋮ A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation ⋮ Identification of the time-dependent source term in a multi-term time-fractional diffusion equation ⋮ Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains ⋮ Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations ⋮ A new treatment based on hybrid functions to the solution of telegraph equations of fractional order ⋮ A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients ⋮ Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation ⋮ A semi-implicit finite difference scheme for the multi-term time-fractional Burgers-type equations ⋮ An inverse space-dependent source problem for a multi-term time fractional diffusion equation ⋮ A transformed \(L 1\) method for solving the multi-term time-fractional diffusion problem ⋮ Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions ⋮ An efficient hybrid numerical scheme for nonlinear multiterm Caputo time and Riesz space fractional-order diffusion equations with delay ⋮ Two finite difference methods based on an H2N2 interpolation for two-dimensional time fractional mixed diffusion and diffusion-wave equations ⋮ Subordination in a class of generalized time-fractional diffusion-wave equations ⋮ Novel numerical analysis of multi-term time fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid ⋮ Identifying a fractional order and a space source term in a time-fractional diffusion-wave equation simultaneously ⋮ Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes ⋮ RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION ⋮ Exact solution of two-term time-fractional Thornley's problem by operational method ⋮ High‐order difference scheme for the solution of linear time fractional klein–gordon equations ⋮ Multi-term time-fractional stochastic differential equations with non-Lipschitz coefficients ⋮ Superconvergence analysis of anH1-Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations ⋮ Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient ⋮ Identification of the zeroth‐order coefficient and fractional order in a time‐fractional reaction‐diffusion‐wave equation ⋮ An inverse problem for a two‐dimensional diffusion equation with arbitrary memory kernel ⋮ A high-order unconditionally stable numerical method for a class of multi-term time-fractional diffusion equation arising in the solute transport models ⋮ Dynamical system method for investigating existence and dynamical property of solution of nonlinear time-fractional PDEs ⋮ Method of separating variables combined with approach of dynamic system for investigating exact solutions of nonlinear time‐fractional models ⋮ Jacobi polynomials for the numerical solution of multi-dimensional stochastic multi-order time fractional diffusion-wave equations
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
- Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
- Solutions of unified fractional Schrödinger equations
- Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
- Implicit difference approximation for the time fractional diffusion equation
- Fractional reaction-diffusion equations
- Solution of generalized fractional reaction-diffusion equations
- Fractional high order methods for the nonlinear fractional ordinary differential equation
- Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method
- Analytical solution for the time-fractional telegraph equation
- Signaling problem for time-fractional diffusion-wave equation in a half-space in the case of angular symmetry
- Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
- Some recent advances in theory and simulation of fractional diffusion processes
- Differentialgleichungen und ihre Anwendungen. Aus dem Engl. übers. von T. Tremmel. (Differential equations and their applications. Translated from the English by T. Tremmel)
- Fractals and fractional calculus in continuum mechanics
- An operational method for solving fractional differential equations with the Caputo derivatives
- The fundamental solutions for the fractional diffusion-wave equation
- Time-fractional telegraph equations and telegraph processes with Brownian time
- Numerical solution of the space fractional Fokker-Planck equation.
- Variable order and distributed order fractional operators
- Solution for a fractional diffusion-wave equation defined in a bounded domain
- Finite difference approximations for fractional advection-dispersion flow equations
- Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
- Numerical method for solving diffusion-wave phenomena
- Analytical solution for the time-fractional telegraph equation by the method of separating variables
- Fundamental solutions to three-dimensional diffusion-wave equation and associated diffusive stresses
- Maximum principle for the generalized time-fractional diffusion equation
- FRACTIONAL DIFFUSIVE WAVES
- Fractional diffusion and wave equations
- Time-fractional Diffusion of Distributed Order
- Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere
- Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
- The fractional diffusion equation
- The fundamental solution of the space-time fractional diffusion equation
- Mechanics with variable-order differential operators
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- Response of a diffusion‐wave system subjected to deterministic and stochastic fields
- Fractional diffusion in inhomogeneous media
- Spectral analysis of fractional kinetic equations with random data.
- The random walk's guide to anomalous diffusion: A fractional dynamics approach