This paper proposes two novel fuzzy fractional PID structures. The tuning of the fuzzy fractional controllers is based on the prior knowledge of fractional-order control tuning rules. The digital implementation of these controllers is also investigated. The effectiveness and robustness of the proposed tuning methodology is illustrated through its application on a fractional-order plant. The sim...

During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o(ḡ) in the coupling constant ḡ. As a first application, based on the RiemannLiouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractiona...

In our earlier work, we introduced a definition for the electric charge "fractional-order" multipoles using the concept of fractional derivatives and integrals [l]. Here, we utilize that definition to introduce a detailed image theory for the two-dimensional (2-D) electrostatic potential distributions in front of a perfectly conducting wedge with arbitrary wedge angles, and for the three-dimens...

a r t i c l e i n f o a b s t r a c t Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the Letter. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only ...

This paper is mainly to deal with the problem of direction of arrival (DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as -stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithm...

System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online identification schemes are also needed for designing adaptive controllers. Real processes are usually of fractional order as opposed to the ideal integral order model...

We study a bound state of fractional D3/D7-branes in the ten-dimensional space IR × IR/Z2 using the boundary state formalism. We construct the boundary actions for this system and we show that higher order terms in the twisted fields are needed in order to satisfy the zero-force condition. We then find the classical background associated to the bound state and show that the gauge theory living ...