This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I, new, general, necessary and sufficient stability conditions are introduced in a unified form for FD/FFD/NFFD-based systems. In Part II, an original, simple, analytical stability criterion is offered for FD-based systems, and the result is used to develop simple, efficient, numerical procedures for testing the asymptotic stability for FFD-based and, in particular, NFFD-based systems. Consequently, the so-called f-poles and f-zeros are introduced for FD-based system and their closed-loop stability implications are discussed

This paper provides a series of new results in both steady-state accuracy and frequency-domain analyses for two Laguerre-based approximators to the Grünwald-Letnikov difference. In a comparative study, the Laguerre-based approximators are found superior to the classical Tustin- and Al-Alaoui-based approximators, which is illustrated in simulation examples.

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

The belt conveyor is the most commonly used conveying equipment in the coal mining industry. As the core part of the conveyor, the belt is vulnerable to various failures, such as scratches, cracks, wear and tear. Inspection and defect detection is essential for conveyor belts, both in academic research and industrial applications. In this paper, we discuss existing techniques used in industrial production and state-of-the-art theories for conveyor belt tear detection. First, the basic structure of conveyor belts is discussed and an overview of tear defect detection methods for conveyor belts is studied. Next, the causes of conveyor belt tear are classified, such as belt aging, scratches by sharp objects, abnormal load or a combination of the above reasons. Then, recent mainstream techniques and theories for conveyor belt tear detection are reviewed, and their characteristics, advantages and shortcomings are discussed. Furthermore, image dataset preparation and data imbalance problems are studied for belt defect detection. Moreover, the current challenges and opportunities for conveyor belt defect detection are discussed. Lastly, a case study was carried out to compare the detection performance of popular techniques using industrial image datasets. This paper provides professional guidelines and promising research directions for researchers and engineers based on the leading theories in machine vision and deep learning.

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.