Sentence examples for principles of fractional from inspiring English sources

The field experiment was designed at two levels and four factors, based on the principles of fractional factorial designs.

Furthermore, in this chapter, the principles of fractional distillation, as well as the computational procedures, are discussed.

Owing to this characteristic, the principles of fractional calculus have played a significant role in improving the modeling techniques for several real world problems [1] [4].

The case is made that the spin-liquid state of a Mott insulator, hypothesized to exist by Anderson and identified by him as the correct context for discussing high-temperature superconductors, occurs in these materials and exhibits the principles of fractional quantization identified in the fractional quantum Hall effect.

They make loans far in excess of the deposits they attract using the principle of fractional reserve banking.

We introduce a new set of indicators measuring internationalized patent applications that are fully coherent with the principle of fractional counting.

The study includes constructing a Lyapunov function, applying a fractional inequality and the comparison principle of linear fractional equation with delay, and obtaining new sufficient conditions.

Sufficient conditions for projective synchronization of master slave systems are achieved by constructing a Lyapunov function, employing a fractional inequality and the comparison principle of linear fractional equation with delay.

In order to obtain general results, an effective controller is designed, a fractional inequality and the comparison principle of linear fractional equation with delay are implemented, and some sufficient conditions are given to ensure that the master slave systems are able to obtain projective synchronization.

We suggest an extension of the standard variational principle for fractional nonlocal media with power-law type nonlocality that is described by the Riesz-type derivatives of non-integer orders.

To establish our main results, we use the Banach contraction mapping principle and the techniques of fractional powers of an operator.