The Whitham-Broer-Kaup equations are modified using local fractional
derivatives, and the equations are then solved by the variational iteration
method. Yang-Laplace transform method is adopted to make the solution
process simpler.
Thermodynamics and fluid mechanics are used to study the mechanical
properties of a class of thermoelastic fluid materials. Using the law of
thermodynamics and the law of conservation of energy, thermal science
analysis of dissipative thermoelastic fluid materials is performed in a
planar 2-D flow field, and a corresponding mathematical model is
established. Fractal theory, operator semi-group theory and fractional
calculus are used to study the overall well-posedness of a dissipative
thermoelastic flow.
This paper, for the first time ever, proposes a Laplace-like integral transform,
which is called as He-Laplace transform, its basic properties are elucidated.
The homotopy perturbation method coupled with this new transform becomes
much effective in solving fractal differential equations. Phi-four equation
with He?s derivative is used as an example to reveal the main merits of the
present technology.
This paper studies a fractal modification of Fokker-Planck equation for a
heat conduction in a fractal medium. Fourier transform and Darboux
transformation are used to solve the equation, some new results are
obtained.
In this paper, we consider the generalized local fractional 2-D Helmholtz equation in steady heat transfer process, which can be used to model the steady-state heat conduction in fractal media. The Yang-Fourier transform and Yang-Laplace transform method are used to solve the equation. The integral expression of the solutions is obtained in detail.
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