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Fractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims to explore a proposed fractional-order differentiated Cournot duopoly game and its discretized game.

Conditions for existence and uniqueness of the proposed game’s solution are derived. The existence of Nash equilibrium point and its local and global stability are obtained. Furthermore, local stability analysis of the discretized game is investigated. The effects of fractional-order on game’s dynamics are examined, along with other parameters of the game, via the 2D bifurcation diagrams in planes of system’s parameters are acquired.

Theoretical and numerical simulation results demonstrate rich variety of interesting dynamical behaviors such as period-doubling and Neimark–Sacker bifurcations, attractors’ crises in addition to chaotic attractors. The results demonstrated that the stability Nash equilibrium point of the game can be lost by period doubling or Neimark–Sacker bifurcations.

Oligopoly games are pivotal in the mathematical modeling of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also macroeconomic analysis of business cycles, innovation and growth.

Although the Cournot game and its variants have attracted great interest among mathematicians and economists since the time of its proposition till present, memory effects in continuous-time and discrete-time Cournot duopoly game have not been addressed yet. To the best of author’s knowledge, this can be considered as the first attempt to investigate this problem of fractional-order differentiated Cournot duopoly game. In addition, studying more realistic models of Cournot oligopoly games plays a pivotal role in the mathematical investigation and better understanding of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also in macroeconomic analysis of business cycles, innovation and growth.

With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).

First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.

The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.

It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.

The purpose of this paper is to study and analyze the effects of fly ash (FA) as a mineral admixture on compressive strength (CS), carbonation resistance and corrosion resistance of reinforced concrete (RC). In addition, the utilization of inexpensive and abundantly available FA as a cement replacement in concrete has several benefits including reduced OPC usage and elimination of the FA disposal problem.

Reinforcement corrosion and carbonation significantly affect the strength and durability of the RC structures. Also, the utilization of FA as green corrosion inhibitors, which are nontoxic and environmentally friendly alternatives. This review discusses the effects of FA on the mechanical characteristics of concrete. Also, this review analyzes the impact of FA as a partial replacement of cement in concrete and its effect on the depth of carbonation in concrete elements and the corrosion rate of embedded steel as well as the chemical composition and microstructure (X-ray diffraction analysis and scanning electron microscopy) of FA concrete were also reviewed.

This review provides a clear analysis of the available study, providing a thorough overview of the current state of knowledge on this topic. Regarding concrete CS, the findings indicate that the incorporation of FA often leads to a loss in early-age strength. However, as the curing period increased, the strength of fly ash concrete (FAC) increased with or even surpassed that of conventional concrete. Analysis of the accelerated carbonation test revealed that incorporating FA into the concrete mix led to a shallower carbonation depth and slower diffusion of carbon dioxide (CO₂) into the concrete. Furthermore, the half-cell potential test shows that the inclusion of FA increases the durability of RC by slowing the rate of steel-reinforcement corrosion.

This systematic review analyzes a wide range of existing studies on the topic, providing a comprehensive overview of the research conducted so far. This review intends to critically assess the enhancements in mechanical and durability attributes (such as CS, carbonation and corrosion resistance) of FAC and FA-RC. This systematic review has practical implications for the construction and engineering industries. This can support engineers and designers in making informed decisions regarding the use of FA in concrete mixtures, considering both its benefits and potential drawbacks.

This study aims to address a comprehensive and integrated investigations pertaining to the preparation of AgNPs with well-defined nano-sized scale using the aforementioned poly (meth acrylic acid [MAA])–chitosan graft copolymer, which is cheap, nontoxic, biodegradable and biocompatible agent as a substitute for the traditionally used toxic reducing agents.

AgNPs are prepared under a range of conditions, containing silver nitrate and poly (MAA)–chitosan graft copolymer concentrations, time, temperature and pH of the preparation medium. To classify AgNPs obtained under the various conditions, ultraviolet–visible spectroscopy spectra and transmission electron microscopy images are used for characterization of AgNPs instrumentally in addition to the visual color change throughout the work. The work was further extended to study the application of the so prepared AgNPs on cotton fabric to see their suitability as antibacterial agent as well as their durability after certain washing cycles.

According to the current investigation, the optimal conditions for AgNPs formation of nearly 3–15 nm in size are 5 g/l, poly (MAA)–chitosan graft copolymer and 300 ppm AgNO₃ in addition to carrying out the reaction at 60°C for 30 min at pH 12. Besides, the application of the so prepared AgNPs on cotton fabric displayed a substantial reduction in antibacterial efficiency against gram-positive and gram-negative bacteria estimated even after 10 washing cycles in comparison with untreated one.

To the best of the authors’ information, no comprehensive study of the synthesis of AgNPs using poly (MAA)–chitosan graft copolymer with a graft yield of 48% has been identified in the literature.

The purpose of this paper is to analyze a parallel system consisting of n dependent components with lifetimes following Weibull distribution. FGM Copula in multivariate case is used to generate the reliability function of the original system. A reduction method is introduced to improve system reliability. Other methods of hot, cold and warm duplication are established to improve system reliability. An application is introduced to show the results and compare between different improvement methods.

In this paper, a study of a parallel system consisting of n dependent and non-identical components is introduced. Reliability function of the original system is derived by using the concepts of copula, subject to Weibull distribution. Reliability function of the original system is improved according to reduction, hot duplication, warm and cold duplication methods. Reliability equivalence factors are introduced to compare between different system designs. Numerical illustration and real-time data application are discussed to show the results obtained in this paper.

Copulas can be used to model the reliability of systems with dependent units.

This paper is original. Improvement of the reliability of dependent systems is not discussed in literature. Copula is a useful tool to analyze the reliability of dependent systems. The introduced model is considered as a generalization of the models discussed in literature.