Sentence examples for system and fractional from inspiring English sources

The effectiveness of the approach is tested on fractional order Rössler system and fractional order Lorenz system.

There are several nonlocal Schrödinger equations such as the Kirchhoff and the Schrödinger-Poisson system, and fractional order differential equations.

The method is successfully applied to modified projective synchronization between fractional order Rössler hyperchaotic system and fractional order Chen hyperchaotic system, and numerical simulations illustrate the effectiveness of the obtained results.

Thus we will apply the theory of linear evolution system and fractional power operators methods to discuss existence, uniqueness, and moment exponential stability of mild solutions to the stochastic partial functional differential equation (1.1).

Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved.

This technique is applied to achieve synchronization between the fractional-order Lorenz systems with different orders, and achieve synchronization between the fractional-order Lorenz system and fractional-order Chen system.

Given the link existing between diffusion-based systems and fractional systems, the transfer functions obtained are fractional with orders multiples of 0.5 [2].

They also have a key role in electric conductance of biological systems and fractional order models of neurons.

For more details of positive solutions of fractional differential systems and fractional BVPs with nonlocal conditions, see [20, 21] and references therein.

Concerning the finite time stability, Ulam's stability and stable manifolds of linear systems, impulsive systems and fractional systems, the methods of fundamental matrix, linear matrix inequality, algebraic inequality and integral inequality are often used to deal with this issue.

It is worth noting that recently much attention has been paid to the distributed-order differential equations and their applications in engineering fields that both integer-order systems and fractional order systems are special cases of distributed-order systems.