A kernel-based method for fractional integro-differential equations with a weakly singular kernel in multi-dimensional complex domains

Azarnavid, Babak

doi:10.1016/j.enganabound.2023.11.015

Engineering Analysis with Boundary Elements

2024

DOI: 10.1016/j.enganabound.2023.11.015

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A kernel-based method for fractional integro-differential equations with a weakly singular kernel in multi-dimensional complex domains

Babak Azarnavid

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Cited by 3 publications

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A numerical investigation of singularly perturbed 2D parabolic convection–diffusion problems of delayed type based on the theory of reproducing kernels

Balootaki,

Ghaziani,

Fardi

et al. 2024

Soft Comput

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A numerical investigation of singularly perturbed 2D parabolic convection–diffusion problems of delayed type based on the theory of reproducing kernels

Balootaki,

Ghaziani,

Fardi

et al. 2024

Soft Comput

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Fourier spectral exponential time-differencing method for space-fractional generalized wave equations

Mohammadi,

Fardi,

Ghasemi

et al. 2024

Opt Quant Electron

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This manuscript deals with a space-fractional generalized wave problem involving the fractional Laplacian operator of order α for 1 < α ≤ 2. We propose an accurate numerical method to solve the mentioned fractional wave problem. The problem is discretized in spatial direction by the Fourier spectral method, and in temporal direction by utilizing the fourth-order exponential time-differencing Runge-Kutta (ETDRK4) method. One of the main features of this method is to reduce the mentioned fractional wave model to an ODE by using the Fourier transform, and then the ETDRK4 method is used to solve this ODE. We define the discrete energy function and check the energy-conserving properties. The convergence of this method is proved. Various numerical experiments are conducted to confirm the accuracy and dependability of the suggested approach.Keywords Generalized wave equation • Fractional Laplacian operator • Fourier spectral method • Fourth-order exponential Runge-Kutta method • convergence.

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A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations

Heydari,

Razzaghi,

Bayram

2025

Results in Physics

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A kernel-based method for fractional integro-differential equations with a weakly singular kernel in multi-dimensional complex domains

Cited by 3 publications

References 31 publications

A numerical investigation of singularly perturbed 2D parabolic convection–diffusion problems of delayed type based on the theory of reproducing kernels

A numerical investigation of singularly perturbed 2D parabolic convection–diffusion problems of delayed type based on the theory of reproducing kernels

Fourier spectral exponential time-differencing method for space-fractional generalized wave equations

A numerical approach for multi-dimensional ψ-Hilfer fractional nonlinear Galilei invariant advection–diffusion equations

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