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Fractional differential equations and inclusions provide appropriate models for describing real world problems, which cannot be described using classical integer order differential equations.
On the other hand, Cauchy problems with nonlocal conditions are appropriate models for describing a lot of natural phenomena, which cannot be described using classical Cauchy problems.
Impulsive differential equations can be used to describe a lot of natural phenomena such as the dynamics of populations subject to abrupt changes (harvesting, diseases, etc)., which cannot be described using classical differential equations.
The contribution of the free carrier species ε fc to the dielectric function can be described using classical Drude approximation [15]: {varepsilon}^{mathrm{fc}}left omega right)=-{varepsilon}_{infty}frac{omega_p^2}{omega left omega +i{gamma}_pright)}, (7 with {omega}_p={left(frac{N{e}^2}{varepsilon_{infty }{varepsilon}_0{m}^{ast }}right)}^{1/2} (8) {gamma}_p=frac{e}{m^{ast}mu } (9).
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The bifurcation and trifurcation of the Kirkendall plane can quantitatively be described using the classical diffusion theory in terms of Kirkendall velocity construction.
Then the possibility exists that not all physical systems traditionally thought to be in the domain of classical mechanics can be described using strictly deterministic models, leading to the need to approach the modeling of such nonlinear systems differently.
A classical mechanical system can be described using a phase space $\Gamma$ with points denoted by $\gamma$.
The mass transport was described using a classical diffusion equation according to Fick's law and a modified Wilke Chang diffusion model.
In this paper, an adaptive nonlinear controller for transient stabilization and voltage regulation of wind power systems based Double Fed Induction Generator (DFIG) in multimachine environment is described using a classical third order dynamical model of the DFIG.
Community membership was described using the classical Jaccard index, while population structure (evaluation of membership and relative abundance of members) was evaluated using the Yue & Clayton index of dissimilarity and Bray-Curtis index.
This phase stability in these multilayers has been described using a model based on classical thermodynamics.
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