A robust numerical method for a fractional differential equation

DOI10.1016/j.amc.2017.08.011zbMath1426.65088OpenAlexW2745857804WikidataQ115361279 ScholiaQ115361279MaRDI QIDQ1740167

Anbo Le, Zhongdi Cen, Aimin Xu

Publication date: 29 April 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2017.08.011

zbMATH Keywords

convergence analysisVolterra integral equationCaputo fractional derivativefractional differential equationadapted mesh

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Fractional ordinary differential equations (34A08)

Related Items

Non-linear boundary value problems involving Caputo derivatives of complex fractional order, Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials

Cites Work

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• Spline collocation for nonlinear fractional boundary value problems
• Piecewise polynomial collocation for linear boundary value problems of fractional differential equations
• A nonpolynomial collocation method for fractional terminal value problems
• An efficient collocation method for a Caputo two-point boundary value problem
• Particle tracking for fractional diffusion with two time scales
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Collocation methods for general Caputo two-point boundary value problems
• Waiting-times and returns in high-frequency financial data: An empirical study
• Modified spline collocation for linear fractional differential equations
• Numerical solution of nonlinear fractional differential equations by spline collocation methods
• Boundary layers in a two-point boundary value problem with a Caputo fractional derivative
• Numerical solution of fractional integro-differential equations by a hybrid collocation method
• Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems
• On the discrete analogues of some generalizations of Gronwall's inequality
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• Limit theorem for continuous-time random walks with two time scales
• A posteriori error analysis for a fractional differential equation
• A finite difference method for a two-point boundary value problem with a Caputo fractional derivative