Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions

DOI10.1016/j.amc.2018.01.030zbMath1426.65216OpenAlexW2794227841MaRDI QIDQ2424840

Yanyan Li

Publication date: 25 June 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2018.01.030

zbMATH Keywords

weakly singular kernelsoperational matrixmodification of hat functionsfractional integro-differential equations

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Singular nonlinear integral equations (45G05) Fractional ordinary differential equations (34A08)

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Cites Work

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• A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions
• Collocation methods for fractional integro-differential equations with weakly singular kernels
• A fractional variational iteration method for solving fractional nonlinear differential equations
• Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
• Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science
• SCW method for solving the fractional integro-differential equations with a weakly singular kernel
• A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels
• Solution of a class of Volterra integral equations with singular and weakly singular kernels
• Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions
• Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel
• Numerical solution of fractional integro-differential equations by a hybrid collocation method
• Solution of fractional differential equations by using differential transform method
• An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel