THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

Xiao-Qun Cao

,

Cheng-Zhuo Zhang

,

Shi-Cheng Hou

,

Ya-Nan Guo

,

Ke-Cheng Peng

online first only

Variational theory for (2+1)-dimensional fractional dispersive long wave equations

ABSTRACT
This paper extends the (2+1)-dimensional Eckhaus-type dispersive long wave equations in continuous medium to their fractional partner, which is a model of nonlinear waves in fractal porous media. The derivation is shown briefly using He's fractional derivative. Using the semi-inverse method, the variational principles are established for the fractional system, which up to now are not discovered. The obtained fractal variational principles are proved correct by minimizing the functionals with the calculus of variations, and might find potential applications in numerical modelling.
KEYWORDS
variational principle, (2+1)-dimensional fractional equations, semi-inverse method, fractal dimension
PAPER SUBMITTED: 1970-01-01
PAPER REVISED: 2020-05-24
PAPER ACCEPTED: 2020-05-24
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200301023C
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Variational theory for (2+1)-dimensional fractional dispersive long wave equations