This paper establishes a fractional-order economic growth model to model the gross domestic product (GDP). The fractional-order model consists of a differential equation of integer and fractional orders, where the GDP is a function of several exploratory variables. An empirical application is adopted using Malaysia\'s GDP data from 1956 to 2018, incorporating exploratory variables such as total population, crude death rate, production of logs, gross fixed capital formation, exports of goods and services, general government final consumption expenditure, private final consumption expenditure, and the impact of investment. Extensive comparisons were carried out to evaluate the modelling performance of the full and reduced fractional-order multiple linear regression models with the benchmark models, namely full and reduced integer-order multiple linear regression models. Results indicate that the reduced fractional-order model with six exploratory variables, excluding the crude death rate and production of logs, predominates other models for the in-sample model fitting based on the Akaike information criterion, coefficient of determination and other criteria. Furthermore, the fractional-order model offers the best-of-sample forecasts evaluated based on the root mean square forecast error and mean absolute forecast error. The application of the Diebold-Mariano test also serves to confirm the superior performance of the suggested fractional-order model, revealing a significant difference in forecasting ability between the fractional-order and integer-order models.

Since the Leibniz rule for integer-order derivatives of the product of functions, which includes a finite number of terms, is not true for fractional-order (FO) derivatives of that, all sliding mode control (SMC) methods introduced in the literature involved a very limited class of FO nonlinear systems. This article presents a solution for the unsolved problem of SMC of a class of FO nonstrict-feedback nonlinear systems with uncertainties. Using the Leibniz rule for the FO derivative of the product of two functions, which includes an infinite number of terms, it is shown that only one of these terms is needed to design a SMC law. Using this point, an algorithm is given to design the controller for reference tracking, that significantly reduces the number of design parameters, compared to the literature. Then, it is proved that the algorithm has a closed-form solution which presents a straightforward tool to the designer to obtain the controller. The solution is applicable to the systems with a mixture of integer-order and FO dynamics. Stability and finite-time convergence of the offered control law are also demonstrated. In the end, the availability of the suggested SMC is illustrated through a numerical example arising from a real system.

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Fractional-order (FO) chaotic systems exhibit random sequences of significantly greater complexity when compared to integer-order systems. This feature makes FO chaotic systems more secure against various attacks in image cryptosystems. In this study, the dynamical characteristics of the FO Sprott K chaotic system are thoroughly investigated by phase planes, bifurcation diagrams, and Lyapunov exponential spectrums to be utilized in biometric iris image encryption. It is proven with the numerical studies the Sprott K system demonstrates chaotic behaviour when the order of the system is selected as 0.9. Afterward, the introduced FO Sprott K chaotic system-based biometric iris image encryption design is carried out in the study. According to the results of the statistical and attack analyses of the encryption design, the secure transmission of biometric iris images is successful using the proposed encryption design. Thus, the FO Sprott K chaotic system can be employed effectively in chaos-based encryption applications.

This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people\'s vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model\'s dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

This paper investigates containment control for fractional-order networked systems. Two novel intermittent sampled position communication protocols, where controllers only need to keep working during communication width of every sampling period under the past sampled position communication of neighbors\' agents. Then, some necessary and sufficient conditions are derived to guarantee containment about the differential order, sampling period, communication width, coupling strengths, and networked structure. Taking into account of the delay, a detailed discussion to guarantee containment is given with respect to the delay, sampling period, and communication width. Interestingly, it is discovered that containment control cannot be guaranteed without delay or past sampled position communication under the proposed protocols. Finally, the effectiveness of theoretical results is demonstrated by some numerical simulations.

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction-diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction-diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R0, the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann-Liouville (R-L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed.

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.