Supervised learning and meshless methods for two-dimensional fractional PDEs on irregular domains

Abbaszadeh, Mostafa; Zaky, Mahmoud A.; Hendy, Ahmed S.; Dehghan, Mehdi

doi:10.1016/j.matcom.2023.08.008

Mathematics and Computers in Simulation

2024

DOI: 10.1016/j.matcom.2023.08.008

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Supervised learning and meshless methods for two-dimensional fractional PDEs on irregular domains

Mostafa Abbaszadeh,

Mahmoud A. Zaky,

Ahmed S. Hendy

et al.

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2024

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Cited by 4 publications

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Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

Heydari,

Razzaghi

2024

Math Methods in App Sciences

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In this study, the stochastic distributed‐order time‐fractional version of the fourth‐order delay sub‐diffusion equation is defined by employing the Caputo fractional derivative. The orthonormal discrete Legendre polynomials, as a well‐known family of discrete polynomials basis functions, are used to develop a numerical method to solve this equation. To employ these polynomials in constructing the expressed approach, the operational matrices of the classical integration, differentiation (ordinary, fractional and distributed‐order fractional), and stochastic integration of these polynomials are extracted. The established method turns solving the introduced stochastic‐fractional equation into solving a more simple linear algebraic system of equations. In fact, by representing the unknown solution in terms of the introduced polynomials and employing the extracted matrices, this system is obtained. The accuracy of the developed algorithm is numerically checked by solving two examples.

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Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

Heydari,

Razzaghi

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations

Taheri,

Aghaei,

Parand

2024

Engineering with Computers

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A mesh-free method using Pascal polynomials for analyzing space-fractional PDEs in irregular biological geometries

Abbaszadeh,

Azis,

Dehghan

2024

Engineering Analysis with Boundary Elements

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Supervised learning and meshless methods for two-dimensional fractional PDEs on irregular domains

Cited by 4 publications

References 46 publications

Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations

A mesh-free method using Pascal polynomials for analyzing space-fractional PDEs in irregular biological geometries

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