Sentence examples for fractional calculations from inspiring English sources

In this paper, α-stable processes involve some fractional calculations.

The results are established by using solution operator theory, fractional calculations and fixed point techniques.

Floating point arithmetic with wide-ranging fractional calculations slowed down the 8-bit bus considerably.

In this section, some basic definitions and lemmas about fractional calculations are presented.

Using fractional calculations, fixed point theorems and the stochastic analysis technique, sufficient conditions are derived to ensure the existence of solutions.

Using fixed point techniques, fractional calculations, stochastic analysis techniques and methods adopted directly from deterministic control problems, R Sakthivel et al. [20] gave a new set of sufficient conditions for approximate controllability of fractional stochastic differential equations.

In Section 2, we recall some concepts and some fractional calculation law and establish preparation results.

Firstly, we introduce fractional-order Lyapunov function based on the definition of fractional calculation and integer order Lyapunov theory.

The fractional calculation is over 300 years old, but only in the last decades its application arisen in many areas of science and engineering.

In this paper, based on fractional calculation, fixed point theorems and the stochastic analysis technique, new existence theorems of solutions for these equations are given.

This fact reflects the ability of fractional calculation to describe different phenomena in different disciplines such as semiconductor, mechanics, chemistry, porous media, anomalous diffusion, etc. [1 7].