Fractional differentiation matrices with applications
From MaRDI portal
Publication:5245264
zbMath1326.65033arXiv1404.4429MaRDI QIDQ5245264
Publication date: 7 April 2015
Full work available at URL: https://arxiv.org/abs/1404.4429
monographalgorithmnumerical methoddiffusion equationfinite elementfinite differencefractional derivativefractional integralCaputo derivativeRiemann-Liouville derivativemultistep methodAdams methodWeyl derivativeadvection-dispersion equations
Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical differentiation (65D25) Numerical integration (65D30) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11) Research exposition (monographs, survey articles) pertaining to real functions (26-02)
Related Items (only showing first 100 items - show all)
بررسی عددی یک طرح تفاضلی جدید روی یک شبکه مدرج برای حل معادلات زیر-انتشار کسری زمانی-مکانی با جوابهای ناهموار ⋮ A linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation: numerical simulations of Gordon-type solitons ⋮ An alternating direction implicit compact finite difference scheme for the multi-term time-fractional mixed diffusion and diffusion-wave equation ⋮ \(L1\)-robust analysis of a fourth-order block-centered Finite difference method for two-dimensional variable-coefficient time-fractional reaction-diffusion equations ⋮ A stable and convergent finite-difference model which conserves the positivity and the dissipativity of Gibbs' free energy for a nonlinear combustion equation ⋮ On the fractional derivatives with an exponential kernel ⋮ Symplectic‐preserving Fourier spectral scheme for space fractional<scp>Klein–Gordon–Schrödinger</scp>equations ⋮ Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost ⋮ A linearized finite difference scheme for time-space fractional nonlinear diffusion-wave equations with initial singularity ⋮ Inverse problem for the Atangana-Baleanu fractional differential equation ⋮ A new class of fuzzy fractional differential inclusions driven by variational inequalities ⋮ Three kinds of discrete formulae for the Caputo fractional derivative ⋮ A superlinear convergence scheme for the multi‐term and distribution‐order fractional wave equation with initial singularity ⋮ Learning parameters of a system of variable order fractional differential equations ⋮ Numerical solution of fractional partial differential equations via Haar wavelet ⋮ Comparative Study of Some Numerical Schemes for a Fractional Order Model of HIV Infection Treatment ⋮ THE DYNAMICS OF HIV/AIDS MODEL WITH FRACTAL-FRACTIONAL CAPUTO DERIVATIVE ⋮ A corrected \(\mathrm{L}1\) method for a time-fractional subdiffusion equation ⋮ A linear Galerkin numerical method for a quasilinear subdiffusion equation ⋮ Analytical and numerical solutions of time-fractional advection-diffusion-reaction equation ⋮ Fractional second linear multistep methods: the explicit forms for solving fractional differential equations and stability analysis ⋮ Assessment of the performance of the hyperbolic-NILT method to solve fractional differential equations ⋮ Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian ⋮ Discretised general fractional derivative ⋮ On the convergence of piecewise polynomial collocation methods for variable-order space-fractional diffusion equations ⋮ Ulam-Hyers stability for an impulsive Caputo-Hadamard fractional neutral stochastic differential equations with infinite delay ⋮ Stability and \(\psi\)-algebraic decay of the solution to \(\psi\)-fractional differential system ⋮ Computation of fractional derivatives of analytic functions ⋮ A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation ⋮ A Fast Temporal Second Order Difference Scheme for the Fractional Sub-diffusion Equations on One Dimensional Space Unbounded Domain ⋮ Enhanced parallel computation for time-fractional fluid dynamics: a fast time-stepping method with Newton-Krylov-Schwarz solver ⋮ A Stable and Convergent Hybridized Discontinuous Galerkin Method for Time-Fractional Telegraph Equations ⋮ Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using \(a\)-polynomials ⋮ Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate ⋮ A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance ⋮ Alternating direction implicit approach for the two-dimensional time fractional nonlinear Klein-Gordon and sine-Gordon problems ⋮ Some existence and uniqueness results for a class of proportional Liouville-Caputo fractional stochastic differential equations ⋮ Ulam type stability for Caputo–Hadamard fractional functional stochastic differential equations with delay ⋮ Time-fractional porous medium equation: Erdélyi-Kober integral equations, compactly supported solutions, and numerical methods ⋮ Collocation-based numerical simulation of fractional order Allen-Cahn equation ⋮ A comparative study on <scp>non‐Newtonian</scp> fractional‐order Brinkman type fluid with two different kernels ⋮ Fast evaluation for magnetohydrodynamic flow and heat transfer of fractional Oldroyd‐B fluids between parallel plates ⋮ Optimal quadrature formula for numerical integration of fractional integrals in a Hilbert space ⋮ Fractional HIV infection model described by the Caputo derivative with real data ⋮ Two-grid \(H^1 \)-Galerkin mixed finite elements combined with \(L1\) scheme for nonlinear time fractional parabolic equations ⋮ Application of Pell collocation method for solving the general form of time-fractional Burgers equations ⋮ Study of fractional-order reaction-advection-diffusion equation using neural network method ⋮ The construction of an optimal fourth-order fractional-compact-type numerical differential formula of the Riesz derivative and its application ⋮ Fractional-order adaptive fault-tolerant control for a class of general nonlinear systems ⋮ Finite volume element methods for two-dimensional time fractional reaction–diffusion equations on triangular grids ⋮ Dynamic response of Mathieu-Duffing oscillator with Caputo derivative ⋮ A fully discrete scheme based on cubic splines and its analysis for time-fractional reaction-diffusion equations exhibiting weak initial singularity ⋮ Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model ⋮ Müntz–Legendre wavelet method for solving Sturm–Liouville fractional optimal control problem with error estimates ⋮ A Compact Difference Scheme for Time-Space Fractional Nonlinear Diffusion-Wave Equations with Initial Singularity ⋮ A Fourier spectral method for the nonlinear coupled space fractional Klein‐Gordon‐Schrödinger equations ⋮ Ulam–Hyers stability of pantograph fractional stochastic differential equations ⋮ Two regularization methods for identifying the source term of Caputo–Hadamard time‐fractional diffusion equation ⋮ High-order schemes based on extrapolation for semilinear fractional differential equation ⋮ Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation ⋮ A fully discrete local discontinuous Galerkin method for variable-order fourth-order equation with Caputo-Fabrizio derivative based on generalized numerical fluxes ⋮ L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions ⋮ Exact solutions of (1+2)-dimensional non-linear time-space fractional PDEs ⋮ ON HADAMARD FRACTIONAL CALCULUS ⋮ Unnamed Item ⋮ A Galerkin finite element scheme for time–space fractional diffusion equation ⋮ Existence of solutions for nonlinear Caputo-Hadamard fractional differential equations via the method of upper and lower solutions ⋮ High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. III. ⋮ General Padé approximation method for time-space fractional diffusion equation ⋮ Effect of parametric excitation on a bifractional-order damped system with a fractional-power nonlinearity ⋮ Regularity of the solution to Riesz-type fractional differential equation ⋮ Local generalization of transversality conditions for optimal control problem ⋮ Conformable Fractional Wave-Like Equation on a Radial Symmetric Plate ⋮ Chaos Detection of the Chen System with Caputo–Hadamard Fractional Derivative ⋮ Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation ⋮ An SEIR Epidemic Model of Fractional Order to Analyze the Evolution of the Covid-19 Epidemic in Argentina ⋮ First-passage properties of asymmetric Lévy flights ⋮ A novel ADI Galerkin spectral element method for the solution of two-dimensional time fractional subdiffusion equation ⋮ Fractional Sturm–Liouville problems for Weber fractional derivatives ⋮ Efficient compact finite difference methods for a class of time-fractional convection–reaction–diffusion equations with variable coefficients ⋮ Fractional collocation methods for multi-term linear and nonlinear fractional differential equations with variable coefficients on the half line ⋮ Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation ⋮ A linearized ADI scheme for two-dimensional time-space fractional nonlinear vibration equations ⋮ Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation ⋮ Fractional-compact numerical algorithms for Riesz spatial fractional reaction-dispersion equations ⋮ Numerical method for system of space-fractional equations of superdiffusion type with delay and Neumann boundary conditions ⋮ Fractional calculus: D'où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016) ⋮ Finite difference methods with non-uniform meshes for nonlinear fractional differential equations ⋮ Existence and numerical simulation of solutions for nonlinear fractional pantograph equations ⋮ Note on weakly fractional differential equations ⋮ DEVELOPMENT AND ANALYSIS OF A SEIR MODEL FOR COVID-19 EPIDEMIC WITH VACCINATION AND NONSINGULAR KERNEL ⋮ DYNAMICS OF COOPERATIVE REACTIONS BASED ON CHEMICAL KINETICS WITH REACTION SPEED: A COMPARATIVE ANALYSIS WITH SINGULAR AND NONSINGULAR KERNELS ⋮ A posteriori error estimation and adaptive strategy for a nonlinear fractional differential equation ⋮ High-order conservative scheme for the coupled space fractional nonlinear Schrödinger equations ⋮ Historical survey: the chronicles of fractional calculus ⋮ Bifurcation analysis of a noisy vibro-impact oscillator with two kinds of fractional derivative elements ⋮ Existence and continuation of solutions of Hilfer-Katugampola-type fractional differential equations ⋮ Fractional-order model of the disease psoriasis: a control based mathematical approach ⋮ Fractional-order harmonic resonance in a multi-frequency excited fractional Duffing oscillator with distributed time delay ⋮ The effects of depletion layer for electro-osmotic flow of fractional second-grade viscoelastic fluid in a micro-rectangle channel
This page was built for publication: Fractional differentiation matrices with applications
