Mittag-Leffler stability of numerical solutions to time fractional ODEs

DOI10.1007/s11075-022-01379-8OpenAlexW4290033617MaRDI QIDQ2691898

Yanyan Li

Publication date: 30 March 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.09620

zbMATH Keywords

Mittag-Leffler stabilitypolynomial decay ratefractional ODEs\(\alpha\)-difference\(\mathcal{L} 1\) schemefractional LMMs

Mathematics Subject Classification ID

Numerical investigation of stability of solutions to ordinary differential equations (65L07) Asymptotic properties of solutions to ordinary differential equations (34D05) Fractional ordinary differential equations (34A08) Numerical analysis (65-XX)

Related Items (4)

Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations ⋮ Superconvergence and postprocessing of collocation methods for fractional differential equations ⋮ \(H^1\)-analysis of H3N3-\(2_\sigma\)-based difference method for fractional hyperbolic equations ⋮ Mittag-Leffler stability of numerical solutions to linear homogeneous time fractional parabolic equations

Uses Software

• RODAS

Cites Work

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• Asymptotic stability of linear fractional systems with constant coefficients and small time-dependent perturbations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations
• Convolution quadrature and discretized operational calculus. I
• Complete monotonicity-preserving numerical methods for time fractional ODEs
• A practical guide to Prabhakar fractional calculus
• Time discretization of fractional subdiffusion equations via fractional resolvent operators
• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• On explicit stability conditions for a linear fractional difference system
• Second-order difference approximations for Volterra equations with the completely monotonic kernels
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• Singularity Analysis of Generating Functions
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral Equations
• A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties
• Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
• An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Long-time behavior of non-local in time Fokker–Planck equations via the entropy method
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Long-time behavior of numerical solutions to nonlinear fractional ODEs
• On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations
• Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations
• The Poisson distribution, abstract fractional difference equations, and stability
• Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions

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