This paper addresses the problem of the fractional sliding mode control (FSMC) for a MEMS optical switch. The proposed scheme utilizes a fractional sliding surface to describe dynamic behavior of the system in the sliding mode stage. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed sliding surface displays better transient per...

This paper addresses the problem of the fractional sliding mode control (FSMC) for a MEMS optical switch. The proposed scheme utilizes a fractional sliding surface to describe dynamic behavior of the system in the sliding mode stage. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed sliding surface displays better transient per...

This paper derives the directional derivative expression of Taylor formula for two-variable function from Taylor formula of one-variable function. Further, it proposes a new concept, fractional directional differentiation FDD , and corresponding theories. To achieve the numerical calculation, the paper deduces power series expression of FDD. Moreover, the paper discusses the construction of FDD...

The aim of the paper is to present the fundamental definitions connected to fractional differentiation and to present an overview of the CRONE approach in the fields of system analysis, modeling and identification, observation and control. Industrial applications of fractional differentiation are also described in this paper. Some recent developments are also presented.

This paper presents a prediction error variance reduction procedure based on fractional digital differentiation with negative order. This reduction is achieved by increasing correlation in the signals. Applications to ECG signals show that savings of more than one bit per residual signal sample can be attained. Keywords—Linear prediction, fractional differentiation, ECG signal.

The sub-title of this presentation could be “The fractional order integrator approach”. Although fractional order differentiation is commonly considered as the basis of fractional calculus, its effective basis is in fact fractional order integration, mainly because definitions, calculation and properties of fractional derivatives and Fractional Differential Systems (FDS) rely deeply on fraction...

There are many resources useful for processing images, most of them freely available and quite friendly to use. In spite of this abundance of tools, a study of the processing methods is still worthy of efforts. Here, we want to discuss the new possibilities arising from the use of fractional differential calculus. This calculus evolved in the research field of pure mathematics until 1920, when ...