Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation

From MaRDI portal

Publication:980168

Jump to:navigation, search

DOI10.1016/j.camwa.2009.08.015zbMath1189.35360OpenAlexW1996576314MaRDI QIDQ980168

Yu. F. Luchko

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2009.08.015

zbMATH Keywords

maximum principle generalized solution Fourier method initial-boundary-value problems Caputo-Dzherbashyan fractional derivative generalized time-fractional diffusion equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Discrete-time orthogonal spline collocation method for a modified anomalous diffusion equation, Three Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domain, Reflected spectrally negative stable processes and their governing equations, Robin coefficient identification for a time-fractional diffusion equation, A generalized quasi-boundary value method for recovering a source in a fractional diffusion-wave equation, Numerical Solution to the Space-Time Fractional Diffusion Equation and Inversion for the Space-Dependent Diffusion Coefficient, The inverse source problem for time-fractional diffusion equation: stability analysis and regularization, Approximate controllability for fractional diffusion equations by interior control, On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operators, On the backward problems in time for time-fractional subdiffusion equations, A mollification regularization method for unknown source in time-fractional diffusion equation, Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation, A new equivalence of Stefan’s problems for the time fractional diffusion equation, Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications, An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point, On the simultaneous reconstruction of the initial diffusion time and source term for the time-fractional diffusion equation, On a weak maximum principle for a class of fractional diffusive equations, Error estimate on the tanh meshes for the time fractional diffusion equation, Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. I: Linear equations, Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation, The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation, Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators, A <scp>kernel‐based pseudo‐spectral</scp> method for <scp>multi‐term</scp> and distributed order <scp>time‐fractional</scp> diffusion equations, Determination of an unknown source term for an inverse source problem of the time-fractional equation, Inverse problem of determining the kernel of integro-differential fractional diffusion equation in bounded domain, Solving time-fractional reaction-diffusion systems through a tensor-based parallel algorithm, An iterative method based on Nesterov acceleration for identifying space-dependent source term in a time-fractional diffusion-wave equation, Dynamical system method for investigating existence and dynamical property of solution of nonlinear time-fractional PDEs, Simultaneous inversion of the space-dependent source term and the initial value in a time-fractional diffusion equation, The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion, Method of separating variables combined with approach of dynamic system for investigating exact solutions of nonlinear time‐fractional models, An inverse source time-fractional diffusion problem via an input-output mapping, On backward fractional pseudo parabolic equation: regularization by quasi-boundary value method, convergence rates, Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems, Difference schemes for partial differential equations of fractional order, Simultaneous inversion for the diffusion and source coefficients in the multi-term TFDE, Numerical Inversion for the Initial Distribution in the Multi-Term Time-Fractional Diffusion Equation Using Final Observations, Generalized Tikhonov method for the final value problem of time-fractional diffusion equation, Maximum principle for certain generalized time and space fractional diffusion equations, Simultaneous inversion for the exponents of the fractional time and space derivatives in the space-time fractional diffusion equation, Stability and convergence of difference schemes approximating a two-parameter nonlocal boundary value problem for time-fractional diffusion equation, Optimal control problem and maximum principle for fractional order cooperative systems, Identification of the degradation coefficient for an anomalous diffusion process in hydrology, An accurate numerical method for solving the generalized time-fractional diffusion equation, Carleman estimate for a fractional diffusion equation with half order and application, Subordination principles for the multi-dimensional space-time-fractional diffusion-wave equation, Anomalous Diffusion: Models, Their Analysis, and Interpretation, The determination of an unknown boundary condition in a fractional diffusion equation, Iterative regularization method for an abstract ill-posed generalized elliptic equation, Maximum principle and its application for the time-fractional diffusion equations, Existence and uniqueness of the solution for a time-fractional diffusion equation, Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder, RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION, Existence and uniqueness results of some fractional boundary value problem, ON WEIGHTED k-FRACTIONAL OPERATORS WITH APPLICATIONS IN MATHEMATICAL PHYSICS, Fractional diffusion-wave equations on finite interval by Laplace transform, Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation, On the initial-boundary-value problem for the time-fractional diffusion equation on the real positive semiaxis, Modeling diffusive transport with a fractional derivative without singular kernel, Space-time fractional diffusion equation using a derivative with nonsingular and regular kernel, Hilfer-Prabhakar derivatives and some applications, Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker-Planck equation, Existence of solutions of the abstract Cauchy problem of fractional order, A numerical scheme for the time-fractional diffusion equation by layer potentials, Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients, Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives, General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems, A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions, Strong maximum principle for fractional diffusion equations and an application to an inverse source problem, Recovery of the solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation, An RBF based finite difference method for the numerical approximation of multi-term nonlinear time fractional two dimensional diffusion-wave equation, On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation, Identification of the zeroth-order coefficient in a time fractional diffusion equation, About the convergence of a family of initial boundary value problems for a fractional diffusion equation of Robin type, Determination of two unknown thermal coefficients through an inverse one-phase fractional Stefan problem, Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations, Numerical solution of time fractional diffusion systems, Cauchy problem for general time fractional diffusion equation, Identifying an unknown source in time-fractional diffusion equation by a truncation method, Generic well-posedness for an inverse source problem for a multi-term time-fractional diffusion equation, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation, Mellin integral transform approach to analyze the multidimensional diffusion-wave equations, On the maximum principle for a time-fractional diffusion equation, Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications, A new contraction condition and its application to weakly singular Volterra integral equations of the second kind, A high-order and extra-dof-free generalized finite element method for time-fractional diffusion equation, Hopf lemma for the fractional diffusion operator and its application to a fractional free-boundary problem, The existence of solution of diffusion equation with the general conformable derivative, Weak solutions to non-homogeneous boundary value problems for time-fractional diffusion equations, Local fractional Fourier series with application to wave equation in fractal vibrating string, Identifying an unknown time-dependent boundary source in time-fractional diffusion equation with a non-local boundary condition, A convergent algorithm for solving higher-order nonlinear fractional boundary value problems, Modeling and simulation of the fractional space-time diffusion equation, Identification of a time-dependent source term in a distributed-order time-fractional equation from a nonlocal integral observation, Numerical solution of time-dependent component with sparse structure of source term for a time fractional diffusion equation, Fractional-parabolic systems, Existence and uniqueness of mild solutions for a final value problem for nonlinear fractional diffusion systems, A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation, Method of separation variables combined with homogenous balanced principle for searching exact solutions of nonlinear time-fractional biological population model, Maximum principles for a class of generalized time-fractional diffusion equations, Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel, Axisymmetric solutions to time-fractional heat conduction equation in a half-space under Robin boundary conditions, Mathematical methods in geothermy, Estimation of parameters in fractional subdiffusion equations by the time integral characteristics method, Stable numerical solution to a Cauchy problem for a time fractional diffusion equation, Solving fractional diffusion equation via the collocation method based on fractional Legendre functions, Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations, Existence and regularity of solutions to time-fractional diffusion equations, Solvability and spectral properties of the boundary value problem for degenerating higher order parabolic equation, Regularization and error estimates for an inverse heat problem under the conformable derivative, Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation, On a backward problem for nonlinear fractional diffusion equations, On the maximum principle for the multi-term fractional transport equation, Separation variable method combined with integral bifurcation method for solving time-fractional reaction-diffusion models, Regularization of inverse source problem for fractional diffusion equation with Riemann-Liouville derivative, Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall's inequality, A modified kernel method for a time-fractional inverse diffusion problem, On the solutions of partial integrodifferential equations of fractional order, A point source identification problem for a time fractional diffusion equation, On existence and uniqueness of solutions for semilinear fractional wave equations, A meshless point collocation method for 2-D multi-term time fractional diffusion-wave equation, Identifying a diffusion coefficient in a time-fractional diffusion equation, Optimization method for determining the source term in fractional diffusion equation, Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation, Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, Strong maximum principle for multi-term time-fractional diffusion equations and its application to an inverse source problem, The finite volume scheme preserving maximum principle for two-dimensional time-fractional Fokker-Planck equations on distorted meshes, On existence and uniqueness of viscosity solutions for second order fully nonlinear PDEs with Caputo time fractional derivatives, Numerical simulations of 2D fractional subdiffusion problems, Existence and uniqueness of the solution to a coupled fractional diffusion system, The explicit formula for solution of anomalous diffusion equation in the multi-dimensional space, Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions, Maximum principle for space and time-space fractional partial differential equations, Simultaneous inversion of time-dependent source term and fractional order for a time-fractional diffusion equation, Determination of Robin coefficient in a fractional diffusion problem, Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation, On time fractional derivatives in fractional Sobolev spaces and applications to fractional ordinary differential equations, Initial-boundary value problems for multi-term time-fractional diffusion equations with \(x \)-dependent coefficients, Error analysis of the Legendre-Gauss collocation methods for the nonlinear distributed-order fractional differential equation, The existeness and uniqueness result of solutions to initial value problems of nonlinear diffusion equations involving with the conformable variable derivative, Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcing, On \(\psi \)-Caputo time fractional diffusion equations: extremum principles, uniqueness and continuity with respect to the initial data, An integral relationship for a fractional one-phase Stefan problem, High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations, On the stability and convergence of difference schemes for the generalized fractional diffusion equation with Robin boundary value conditions, Regularity of solutions to space-time fractional wave equations: A PDE approach, Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations, Mathematik als Schlüsseltechnologie zum Verständnis des Systems ``Tiefe Geothermie, A numerical solution strategy based on error analysis for time-fractional mobile/immobile transport model, Boundary value problems for the diffusion equation of the variable order in differential and difference settings, Time-fractional diffusion equation in the fractional Sobolev spaces, Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density, Upon solutions to the transonic plane-parallel gas flows, Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications, On the convergence of difference schemes for fractional differential equations with Robin boundary conditions

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:980168&oldid=12970044"