Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order
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DOI: 10.1016/j.chaos.2022.111856
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- Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
- Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
- Qu, Haidong & She, Zihang & Liu, Xuan, 2021. "Neural network method for solving fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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Cited by:
- Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.
- Ma, Zhiying & Hou, Jie & Zhu, Wenhao & Peng, Yaxin & Li, Ying, 2023. "PMNN: Physical model-driven neural network for solving time-fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
- Abdelkader Moumen & Abdelaziz Mennouni, 2022. "A New Projection Method for a System of Fractional Cauchy Integro-Differential Equations via Vieta–Lucas Polynomials," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
- Hou, Jie & Ma, Zhiying & Ying, Shihui & Li, Ying, 2024. "HNS: An efficient hermite neural solver for solving time-fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
- Liang Song & Shaodong Chen & Guoxin Wang, 2023. "Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
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Keywords
Variable-order fractional derivative; Neural network method; Fractional advection-diffusion equation;All these keywords.
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