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In this paper, we aim to establish the uniform stability criteria for fractional‐order time‐delayed gene regulatory networks with leakage delays (FOTDGRNL). First, we establish the existence and uniqueness of the considered systems by using the Banach fixed point theorem. Second, the delay‐dependent uniform stability and robust uniform stability of FOFGRNLT are investigated with the help of certain analysis techniques depending on equivalent norm techniques. Finally, the paper comes up with two numerical examples to justify the applicability of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we dedicate to investigate complete synchronization of discrete‐time fractional‐order Cohen–Grossberg neural networks (DFCGNNs) with time delays. In order to resolve the problem, we have made the following efforts. First, we establish a fractional‐order convergence principle by employing nabla Laplace transform and analysis techniques. Next, an adaptive nonlinear controller is designed, and then several complete synchronization criteria of DFCGNNs are obtained with the help of inequality techniques and convergence principle we newly establish. Finally, a numerical example is presented to show the validity of theorical results we derive. [ABSTRACT FROM AUTHOR]

This paper investigates the H∞$$ {H}_{\infty } $$ filtering for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of H∞$$ {H}_{\infty } $$‐norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the H∞$$ {H}_{\infty } $$ filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of fractional‐order quaternion‐valued neural networks with discrete and distributed delays by direct method. We first investigate some properties of Besicovitch almost periodic functions, including the composition theorem with deviating arguments. Then, we obtain the existence and uniqueness of Besicovitch almost periodic solutions for such class of networks by considering an appropriate Banach space and using the contraction mapping principle. Furthermore, by making use of a generalized Gronwall inequality, we gain the finite‐time stability of the Besicovitch almost periodic solution. Even if the network under consideration degenerates into a real‐valued or complex‐valued networks, the results of this paper are still brand new. Finally, we use a numerical example to show the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

ABSTRACT Wireless power transfer (WPT) is an emerging technology that enables the wireless transfer of electrical energy from power supplies to electrical equipment. It has been widely used in electric vehicles, mobile phones, household appliances, medical devices, and other fields. However, the frequency splitting and bifurcation phenomena existing in WPT systems are the fundamental obstacles and challenges that affect the effective operation of WPT systems. In this paper, a method based on the fractional‐order circuit is proposed to simultaneously suppress the frequency splitting and bifurcation phenomena by changing the order of fractional‐order capacitor. By replacing the compensation capacitor in the transmitter of the traditional WPT system with a fractional‐order capacitor, a fractional‐order WPT system is formed. Then, using fractional calculus and circuit theory, the mathematical model of the proposed WPT system containing a fractional‐order capacitor is established, and the frequency splitting and bifurcation phenomena are analyzed. The theoretical results show that the frequency splitting and bifurcation phenomena are suppressed only by adjusting the order of fractional‐order capacitor, and the output power of the original resonant frequency is improved. Finally, the experimental prototype is implemented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the parameter identification issue of electrochemical double layer capacitors (EDLCs). The superiority of the fractional‐order equivalent impedance model is revealed mathematically and electrochemically by analyzing the variation trends of different models and the general electrochemical impedance spectroscopy (EIS) of EDLCs. Since the fractional‐order models can be used to describe the long‐tailed variation trend of the EIS of EDLCs in the low‐frequency band and can reflect the self‐charging phenomenon of EDLCs, the accuracy of parameter identification can be ensured. In addition, the idea of Levy flight is introduced and combined with the intelligent algorithms in the parameter identification process, thus accelerating the convergence rate of the parameter identification process. At the same time, the problem of nonconvex fitness function falling into local optimum can be solved. To confirm the effectiveness and superiority of this work, we provided diverse test scenarios. We used three different types of EDLCs, while a series of scenarios with or without Levy flight strategy were included in the tests. In our work, we compared not only the accuracy of the parameter identification but also the convergence rate of the identification process. The test results show that, by applying the proposed scheme, the sum of square error (SSE) between experiments and parameter identification results is less than 1.9%. Moreover, the convergence rate of the parameter identification process was improved. In extreme conditions, the convergence rate is 1287% faster than the schemes without Levy flight strategy. [ABSTRACT FROM AUTHOR]

In this paper, the stability and stabilization problems for fractional‐order time‐varying delay systems are investigated. Firstly, by casting the stability problem as one of robust stability analysis problems and utilizing the small gain theorem, an order‐dependent and delay‐dependent stability condition for fractional‐order time‐varying delay systems is developed. Taking advantage of the information of order and delay, the stability condition is less conservative than the existing results. Then, state feedback controllers that stabilize fractional‐order time‐varying delay systems are developed. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones. [ABSTRACT FROM AUTHOR]

In a magnetic coupled wireless power transfer (WPT) system, reflected impedance is the equivalent impedance reflected from receiver to transmitter, playing an important role in transfer efficiency. However, the study on the reflected impedance of fractional‐order magnetic coupled WPT systems is lacking. Therefore, this paper analyzes the reflected impedance characteristics of fractional‐order WPT systems. Based on circuit theory, comparative investigations about the reflected impedance of fractional‐order and integer‐order WPT systems are performed. It is demonstrated that the reflected impedance of the fractional‐order WPT system has a stronger anti‐interference ability against the shift of coupling coefficient and resonant frequency than the integer‐order WPT system. The experimental results verify the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper deals with the problems of quasi‐projective synchronization (QPS) and finite‐time synchronization (FTS) for a kind of delayed fractional‐order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite‐time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols. [ABSTRACT FROM AUTHOR]

Summary: The grid‐connected inverter (GCI) based on the fractional‐order LCL (FOLCL) filter can achieve good attenuation of resonant peak and simplify the control system design by omitting the capacitor current feedback as long as the orders of the inductor and capacitor are set appropriately. This paper investigates the parameter design methods of four types of controllers based on a single‐phase FOLCL‐type GCI without capacitor current feedback; the four controllers are the integer‐order proportional integral controller, fractional‐order proportional integral controller, integer‐order proportional resonance controller, and fractional‐order proportional resonance controller. Closed‐loop constraints based on steady‐state error, phase margin, and gain margin are given to design the specific parameters of each controller. The methods can accurately and quickly obtain the appropriate controller parameters to meet the system performance requirements without repeated trial and error. Simulations and hardware‐in‐the‐loop experiments verify the validity of the theoretical analyses. [ABSTRACT FROM AUTHOR]

Fractional order calculus, with its inheritance and infinite memory properties, is a promising research area in information processing and modeling of certain physical systems, system identification, and control. In this paper, a fractional‐order gradient descent method is proposed for backpropagation training of multilayer feedforward neural networks. In particular, the Caputo derivative is used to define the measurement function and consider the L1/2$L_{1/2}$ smooth regular term. In addition, the monotonicity of the error function and the strong (weak) convergence theorem of the algorithm are rigorously proved. Finally, numerical experiments prove the correctness and effectiveness of the algorithm theory. [ABSTRACT FROM AUTHOR]

In this paper, open loop and closed loop PDα‐type fractional‐order iterative learning control algorithms with fixed topology for the fractional‐order distributed multi‐agent systems are proposed. In the sense of Lebesgue‐p norm, the convergences of the proposed methods are discussed by using the generalized Young inequality of convolution, and their convergence conditions are presented. The proposed algorithm extends the application scope of traditional iterative learning control theory. Theoretical analysis shows that by selecting the appropriate learning gain matrix, the output of each agent can completely track the desired trajectory in a limited time interval as the number of iterations increases. The feasibility and theoretical correctness of the presented algorithm are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This article mainly investigates the quasi‐uniform stability of fractional‐order neural networks with time discrete and distributed delays (FONNDDDs). First, a novel fractional‐order Gronwall inequality with discrete and distributed delays (FOGIDDDs) is established; it can be used to study the stability of a variety of fractional‐order systems with discrete and distributed delays (FOSDDDs). Second, on the basis of this inequality and Leray‐Schauder alternative theorem, the existence and uniqueness results for the FONNDDDs are proved. Third, an improved criterion for the quasi‐uniform stability of FONNDDDs is obtained in terms of this inequality. Ultimately, one numerical example is provided to expound the effectiveness and the superiority of the proposed result. [ABSTRACT FROM AUTHOR]

This manuscript examines global dissipativity and synchronization criteria for time‐delayed fractional‐order gene regulatory networks (FGRNs). The Lyapunov stability theory is used to examine a class of FGRNs with delay arguments that are inspired by the integer‐order delayed gene regulatory network model. Some sufficient criteria are established using the fractional‐order comparison principle and stability theorem for fractional‐order time‐delayed systems to ensure the global dissipativity solution of FGRNs with both feedback regulation and translation time delays. Furthermore, for FGRNs, the global asymptotic synchronization condition is accomplished by constructing an adaptive delayed feedback control method for the master–slave system. Finally, two numerical examples are provided to demonstrate the applicability and superiority of the conclusions obtained. [ABSTRACT FROM AUTHOR]

The finite‐time stability (FTS) of fractional‐order delayed Cohen–Grossberg neural networks (FODCGNNs) with the order ℘ ∈ (1, 2) is investigated in this study. Based on the fractional‐order delayed Gronwall inequality (FODGI), a new sufficient condition to guarantee the FTS of FODCGNNs is established, which reduces the conservation of the existing criterion. Finally, one numerical example is exhibited to illustrate the effectiveness and less conservativeness of the obtained results. [ABSTRACT FROM AUTHOR]