Numerical approaches to Caputo-Hadamard fractional derivatives with applications to long-term integration of fractional differential systems

DOI10.1016/J.CNSNS.2021.106096OpenAlexW3208090187MaRDI QIDQ2060665

Yanyan Li

Publication date: 13 December 2021

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

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.106096

zbMATH Keywords

long-term integrationCaputo-Hadamard derivativeL2-1\(_\sigma\) formulaH2N2 formulaL1-2 formula

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Functions of one variable (26Axx)

Related Items (13)

On some Volterra-Fredholm and Hermite-Hadamard-type fractional integral inequalities ⋮ HADAMARD FRACTIONAL CALCULUS ON TIME SCALES ⋮ A class of time-fractional diffusion equations with generalized fractional derivatives ⋮ The finite-time blow-up for semilinear fractional diffusion equations with time \(\psi\)-Caputo derivative ⋮ Finite difference schemes for time-space fractional diffusion equations in one- and two-dimensions ⋮ A Galerkin finite element method for the space Hadamard fractional partial differential equation ⋮ Discretised general fractional derivative ⋮ Enhanced parallel computation for time-fractional fluid dynamics: a fast time-stepping method with Newton-Krylov-Schwarz solver ⋮ Numerical solutions of Hadamard fractional differential equations by generalized Legendre functions ⋮ Alternating direction implicit approach for the two-dimensional time fractional nonlinear Klein-Gordon and sine-Gordon problems ⋮ Mathematical analysis of the Hadamard-type fractional Fokker-Planck equation ⋮ On blow-up for a time-space fractional partial differential equation with exponential kernel in temporal derivative ⋮ Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative

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• Finite difference/spectral approximations for the time-fractional diffusion equation
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