Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations

DOI10.1016/j.cnsns.2018.11.004zbMath1464.65083arXiv1902.09806OpenAlexW2899549069WikidataQ128973159 ScholiaQ128973159MaRDI QIDQ2207302

Roberto Garrappa

Publication date: 22 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.09806

zbMATH Keywords

convergencenonlocalitynumerical methodsfractional differential equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Blow-up in context of PDEs (35B44) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11)

Related Items (11)

A new numerical method for solving semilinear fractional differential equation ⋮ A fully explicit variational integrator for multidimensional systems of coupled nonlinear fractional hyperbolic equations ⋮ Cagan model of inflation with power-law memory effects ⋮ Generalized Mittag-Leffler quadrature methods for fractional differential equations ⋮ Dynamical analysis and anti-oscillation-based adaptive control of the FO arch MEMS with optimality ⋮ Corrigendum to: ``Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations ⋮ Leibniz type rule: \(\psi\)-Hilfer fractional operator ⋮ On the properties of some operators under the perspective of fractional system theory ⋮ General fractional calculus and Prabhakar's theory ⋮ Neglecting nonlocality leads to unrealistic numerical scheme for fractional differential equation: Fake and manipulated results ⋮ Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative

Uses Software

• ML

Cites Work

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• Too much regularity may force too much uniqueness
• On the order of the error in discretization methods for weakly singular second kind Volterra integral equations with non-smooth solutions
• Numerical solution of fractional differential equations: a survey and a software tutorial
• A comment on some new definitions of fractional derivative
• Detailed error analysis for a fractional Adams method
• A predictor-corrector approach for the numerical solution of fractional differential equations
• No nonlocality. No fractional derivative
• Trapezoidal methods for fractional differential equations: theoretical and computational aspects
• Local fractional derivatives of differentiable functions are integer-order derivatives or zero
• Short memory principle and a predictor-corrector approach for fractional differential equations
• Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
• Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense
• Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions
• Approximate product-integration
• The numerical solution of fractional differential equations: speed versus accuracy

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