A fast and high-order numerical method for nonlinear fractional-order differential equations with non-singular kernel

DOI10.1016/j.apnum.2021.01.013zbMath1458.65119arXiv2010.02664OpenAlexW3125984237WikidataQ112880258 ScholiaQ112880258MaRDI QIDQ1995959

Seyeon Lee, Junseo Lee, Bongsoo Jang, Hyunju Kim

Publication date: 2 March 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.02664

zbMATH Keywords

predictor-corrector algorithmCaputo fractional derivativeGronwall's inequalityCaputo-Fabrizio fractional derivative

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical interpolation (65D05) Fractional partial differential equations (35R11) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

A high order numerical method for solving Caputo nonlinear fractional ordinary differential equations ⋮ A new fast predictor-corrector method for nonlinear time-fractional reaction-diffusion equation with nonhomogeneous terms

Uses Software

• Fractional Order Chaotic Systems

Cites Work

• Unnamed Item
• Too much regularity may force too much uniqueness
• A spectral collocation method for a weakly singular Volterra integral equation of the second kind
• Fractional-order nonlinear systems. Modeling, analysis and simulation
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation
• Robust IMEX schemes for solving two-dimensional reaction-diffusion models
• Solution of pattern waves for diffusive Fisher-like non-linear equations with adaptive methods
• Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative
• Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
• Chaos, fractional kinetics, and anomalous transport
• A predictor-corrector approach for the numerical solution of fractional differential equations
• A new derivative with normal distribution kernel: theory, methods and applications
• Efficient numerical approach for solving fractional partial differential equations with non-singular kernel derivatives
• Why fractional derivatives with nonsingular kernels should not be used
• Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives
• A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative
• A high-order predictor-corrector method for solving nonlinear differential equations of fractional order
• Piecewise spectral collocation method for system of Volterra integral equations
• A high order schema for the numerical solution of the fractional ordinary differential equations
• Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels
• Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
• Weakly Singular Discrete Gronwall Inequalities
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• Piecewise Polynomial Collocation Methods for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels
• Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions
• Piecewise Legendre spectral-collocation method for Volterra integro-differential equations
• Advances in Fractional Calculus