Supplement a high-dimensional time fractional diffusion equation

Liu, Jian‐Gen; Geng, Fazhan; Li, Xin

doi:10.1016/j.aej.2023.05.090

Cited by 1 publication

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“…The fractional symmetry analysis scheme is an effective tool to deal with fractional differential equations, specifically the higher-dimensional nonlinear models [17][18][19][20][21][22][23][24]. For example, Adeyemo et al [17] studied the time fractional (3 + 1)-dimensional generalized Zakharov-Kuznetsov equation type I, Liu et al [18][19][20][21] researched the higher-dimensional KdV-type equation, dissipation Burgers equation, and diffusion equation, Sahoo et al [22] discussed the (3 + 1)-dimensional time-fractional mKdV-ZK equation, and Zhuo et al [23] analyzed the generalized (4 + 1)dimensional time-fractional Fokas equation, Zhu et al [24] considered the time-fractional (2 + 1)-dimensional Hirota-Satsuma-Ito equations. Therefore, we hope to find more novel results through this effective tool, laying the foundation for our deeper understanding of this model.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation

Liu,

Feng

2024

Fractal Fract

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In this article, we analyzed the time fractional higher-dimensional nonlinear modified model of wave propagation, namely the (3 + 1)-dimensional Benjamin–Bona–Mahony-type equation. The fractional sense was defined by the classical Riemann–Liouville fractional derivative. We derived firstly the existence of symmetry of the time fractional higher-dimensional equation. Next, we constructed the one-dimensional optimal system to the time fractional higher-dimensional nonlinear modified model of wave propagation. Subsequently, it was reduced into the lower-dimensional fractional differential equation. Meanwhile, on the basis of the reduced equation, we obtained its similarity solution. Through a series of analyses of the time fractional high-dimensional model and the results of the above obtained, we can gain a further understanding of its essence.

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