Sentence examples for models of fractional from inspiring English sources

It allow us to get more correct models of fractional nonlocal media by fractional variational principle.

El-Karamany and Ezzat (2011) introduced two general models of fractional heat conduction law for a non-homogeneous anisotropic elastic solid.

In this paper, we presented an effective numerical method and its application to solution of linear and nonlinear models of fractional order used in bioengineering applications.

As a result, proposed fractional variational principle allows us to get the Euler-Lagrange equations that are directly connected with microstructural lattice models of fractional nonlocal media [31 34, 40], and the lattice field theories [35, 38].

Petrological models of fractional crystallization suggest deep pressures of crystallization of > 0.4 GPa for most of the samples, which is in good agreement with similar calculations from slow/ultra-slow spreading ridges and require a relatively hydrated (~ 0.5 wt.% H2O) MORB-like source composition.

In Section 2, some necessary theories and the mathematical models of fractional-order and integer-order systems are given.

The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications.

The Oustaloup approximation is employed to derive the approximate model of fractional order system.

Therefore, it is necessary to consider the time-delay effect in the mathematical modeling of fractional differential equations.

Therefore, it is essential to consider the time-delay effect in the mathematical modeling of fractional differential equations.

A closed form formula on the error of approximation is derived to demonstrate the accuracy of the proposed discretization model of fractional derivatives.