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Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. This phenomenon is observed in oceanographic research involving sea surface and internal waves, where intricate multi-dimensional interactions play a crucial role. In this work, we use the improved modified extended tanh function method for the first time to extract the exact solutions of the eighth-order (3+1)-dimensional Kac-Wakimoto equation, which describes the dynamics of fields and the structure of solutions in various physical and mathematical contexts. The proposed method is simple and quick to execute, and it offers more innovative solutions than other methods. As a consequence, through the donation of suitable assumptions for the parameters, some new solutions for dark and singular soliton, as well as Jacobi elliptic, exponential, hyperbolic, and singular periodic forms, are developed. Furthermore, to enhance understanding, graphical representations of certain solutions are included.

In this study, we introduce the new (3+1)-dimensional $ \beta $-fractional Boussinseq-Kadomtsev-Petviashvili (KP) equation that describes the wave propagation in fluid dynamics and other physical contexts. By using the modified extended direct algebraic method, we investigate diverse wave solutions for the proposed fractional model. The acquired solutions, include (dark, bright) soliton, hyperbolic, rational, exponential, Jacobi elliptic function, and Weierstrass elliptic doubly periodic solutions. The primary objective is to investigate the influence of fractional derivatives on the characteristics and dynamics of wave solutions. Graphical illustrations are presented to demonstrate the distinct changes in the amplitude, shape, and propagation patterns of the soliton solutions as the fractional derivative parameters are varied.

Abstract In order to maximize the electricity supply from clean energy sources, the goal of the smart power system is to unite all renewable energy sources. The goal of the present study is to use three optimization techniques, artificial rabbits optimization algorithm (ARO), grey wolf optimizer (GWO), and whale optimization algorithm (WOA), to reduce the cost of electricity (COE) while improving the reliability of the power supply for rural areas. While using the same control variables for the optimization methods and load profile, various hybrid system configurations are explored. Photovoltaic, wind turbine, fuel cell, and electrolyser systems are all involved in the proposed hybrid renewable system. The ARO methodology is more effective than the GWO, WOA, and PSO procedures in terms of net present cost (NPC) and cost of energy (COE) generation, according to data comparing the three optimization techniques with the traditional Particle Swarm Optimization (PSO) method. The proposed ARO reached a value of COE of 0.4412$/kWh compared to 0.4438$/kWh for GWO, 0.4443$/kWh for WOA, and 0.44378$/kWh for PSO.

The coupled higher-order nonlinear Schrödinger equations (CHNLSEs) are investigated in this paper. This model mimic the actuation of the solitons through multimode fibers. The technique of improved modified extended tanh function is used to conduct the study. Many exact solutions are achieved like bright solitons, dark solitons and singular solitons. Moreover, singular periodic solutions, Weierstrass elliptic function solutions, hyperbolic and Jacobi elliptic solutions are raised. Using 3D and 2D graphs, the physical behavior of the produced solutions is illustrated.

The nonlinear fractional Klein–Fock–Gordon (KFG) equation represents an advanced theoretical physics and applied mathematical tool that provides a more extraordinary framework for studying fields with complex and non-standard behaviors. Here, we aim to delve into the new wave profiles of this fractional KGF equation. Initially, this system is successfully converted into an ordinary differential equation (ODE) with the help of wave conversion, and the ODE is solved through the unified and unified solver techniques for the first time. In addition, the 3D and 2D plots of these solutions are drawn using a mathematical software package for different parameters with different values. Therefore, some unique waveforms can be found in these solutions. Moreover, stability and multistability analyses are prepared and shown graphically to confirm the converging limitations of appropriate parameters. This work will be practiced more effectively in future research on nonlinear partial differential models.

This study is focusing on the integrable (3+1)-dimensional equation that combines the potential Kadomtsev-Petviashvili (pKP) equation with B-type Kadomtsev-Petviashvili (BKP) equation, also known as the pKP-BKP equation. The idea of combining integrable equations has the potential to produce a variety of unexpected outcomes such as resonance of solitons. This article provides a wide range of alternative exact solutions for the pKP-BKP equation in three dimensional form, including dark solitons, singular solitons, singular periodic solutions, Jacobi elliptic function (JEF) solutions, rational solutions and exponential solution. The improved modified extended (IME) tanh function method is employed to investigate these solutions. All of the obtained solutions for the investigated model are presented using the Wolfram Mathematica program. To further help in understanding the solutions' physical characteristics and dynamic structure, the article provides visual representations of some derived solutions using 2D representation in addition to the 3D graphs via symbolic computation. This article aims to use a potent strategy using a powerful scheme to derive different solutions with various structures. Additionally, the results greatly improve and enhance the literature's solutions to a combined pKP-BKP equation and allow deep understanding of the nonlinear dynamic system through different exact solutions.

Abstract One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results.

Abstract The motivation behind this work is the preparation of polyurethane-magnesium aluminum layered double hydroxide (PU-LDH) nanocomposite and its application as a coating for steel protection. The coating was prepared with different doses of LDH, ranging from 0 to 2% of the coating weight. The effect of different concentrations on the mechanical, adhesion, and surface properties of PU coating is studied. Firstly, LDH was prepared via the coprecipitation process and then distributed in PU matrix. The nanocomposites were then crosslinked in the form of coating layers on steel. The preparation of the thermally stable crystalline LDH nanoparticles with 89 nm particle size was confirmed by FTIR, XRD, DLS, and TGA. SEM photos showed the dispersed and intercalated structure. The coating characteristics demonstrate that addition of LDH decreased the drying time and increased the dry film thickness of PU up to 1.5% due to the crosslinking between the large surface area nanofiller and polyurethane matrix. Furthermore, the prepared LDH nanofiller increased the adhesion strength, impact resistance, abrasion resistance, modulus, and flexibility of PU due to the strong polymeric network structure. The 2% nanocomposite coating shows poor properties due to the excess concentration and heterogeneous dispersion of nanoparticles within the PU polymer. The resistance to fire and some chemicals was supported by the thermally and physically stable LDH nanoclay. The former characterizations state that the proposed PU-LDH nanocomposite is an enhanced and applicable coating.

We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. These results realize the stability of the nonlinear waves' propagation in a high-nonlinear-dispersion medium that is illustrated using 2D and 3D visuals and contour graphical diagrams of the output solutions. This research focused on determining exact soliton solutions under certain parameter conditions and evaluating the stability and reliability of the soliton solutions based on the used modified extended direct algebraic method. This will be useful for many various domains in technology and physics, such as biology, optics, and plasma physical science. At the end, we use modulation instability analysis to assess the stability of the wave solutions obtained.

We investigated the dynamics of highly dispersive nonlinear gap solitons in optical fibers with dispersive reflectivity, utilizing a conformable fractional derivative model. The modified extended direct algebraic method was employed to obtain various soliton solutions, including bright solitons and singular solitons, as well as hyperbolic and trigonometric solutions. The key findings demonstrated that the fractional derivative parameter (α) can effectively control the wave propagation, causing a shift in the wave signal while maintaining the same amplitude. This is a novel contribution, as the ability to control soliton properties through the conformable derivative is explored for the first time in this work. The results showcase the significant influence of fractional derivatives in shaping the characteristics of the soliton solutions, which is crucial for accurately modeling the dispersive and nonlocal effects in optical fibers. This research provides insights into the potential applications of fractional calculus in the design and optimization of photonic devices for optical communication systems.

Abstract The aim is to develop new fiber-reinforced polymer (FRP) water pipe by activating fiber glass (FG) by vinyltriethoxysilane (VS) getting vinylsilane-activated FG (AFG) for filling vinylester (VE) via continuous winding to make a novel VE-AFG composite. The novelty of this work is the activation of fiber glass by vinylsilane as a single filler in vinylester and compounding them via a two-dimensional continuous winding process for the first time. The crosslinking occurred in the AFG/VE/curing agent system after activation. The activated composites increased thermal stability; 25% VE-AGF increased the degradation temperatures at 10%, 25%, and 50% weight loss by 73.3%, 10%, and 7.2%. With the activated 20% composite, values of axial strength, hoop strength, and hardness were developed by 6.3%, 2%, and 8.7%, respectively. The decay resistance to different microorganisms was increased with VE-AFG composites as a result of a sharp decrease in biodegradability percentages. The activated composites are stable toward water absorption; the least percentage was recorded by 25% VE-AFG, which minimized the water absorptivity by more than 62%. The reported characterization sentence approves enhancement of thermal, physical, and mechanical stability of sustainable vinylester-fiber glass composites manufactured by continuous winding; this is recommended for application in water pipe systems.

Abstract As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic delay differential equations driven by Lévy noise. The link between the averaged equation solutions and the equivalent solutions of the original equations is shown in the sense of mean square. To achieve the intended outcomes, fractional calculus, semigroup properties, and stochastic analysis theory are used. We also provide an example to demonstrate the practicality and relevance of our research.

Currently, there is a lack of research on how fire affects the shear capacity of reinforced concrete (RC) beams reinforced with glass fiber-reinforced polymer (GLASS-F.R.P.) bars. This study examines the shear performance of beams reinforced with GLASS-F.R.P. bars when exposed to fire. Twelve RC beam specimens were fabricated for this purpose, exposed to fire, and then subjected to four-point bending until failure. The specimens had a total span of 1700 mm and a concrete cross-section measuring 150 mm wide and 300 mm deep. The parameters were the ratio of reinforcements and the duration of the firing. The test findings indicate that the concrete's ability to resist shear forces is affected by both the ratio of reinforcement and the length of time it is exposed to fire. Increasing the amount of flexural reinforcement specifically enhances the shear capability. On the other hand, increasing the amount of time that something is subjected to fire decreases its ability to withstand force. It has been noted that the shear design equations from ACI 440.11–22 (ACI-22) and ECP 208–05 (ECP-05) tend to be conservative for elements regardless of fire exposure. In contrast, the shear design methodology described in CSA S806–12 (CSA-12) stands out as the most accurate approach for predicting shear capacity.

This study tackles a nonlinear Schrödinger’s equation in three dimensions, using three dispersive components of fourth order, often resulting in pure-quartic solitons. Pure-quartic bullets are known to deviate from conventional solitons due to their balance of fourth-order dispersion and nonlinearity. As bright and dark optically modulated bullets, we derive many solutions. Experiments on bullet transmission using optical nanofibers can benefit from the solutions found. Our creative solutions are produced by implementing the well-known scheme which is the improved modified extended tanh-function scheme. We find novel kinds of solutions (dark, bright, singular solitons, exponential, singular periodic, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic functions) that make their originality for the problem at hand evident by using the previously described approach. Contour plots and 2D and 3D visualizations in Wolfram Mathematica software are used to show how the well-furnished results propagate for various values of the necessary free parameters. The results demonstrate the computational processes’ precise, well-informed, and efficient nature. Through their integration with representational computations, they may be applied to increasingly complex phenomena. This work constitutes a major advancement in our comprehension of the intricate and erratic behavior of this mathematical model.

Among the all possible isomers of triazolopyrimidines, 1,2,4-triazolo[1,5-a]pyrimidines are the most important isomers owing to their vast activities in agriculture and medicinal chemistry. Herein, we present an overview of the most used synthetic pathways of this scaffold to assist researchers design new drug molecules with expected pharmacological activities

Thirty dairy buffaloes were used for 90 days to evaluate the impact of a novel protein source (HI-PRO®), a feed alternative rich in protein (made from Saccharomyces and Bacillus), on the productivity of nursing buffaloes. The nursing water buffaloes had an average weight of 550 ± 11.2 kg. The treatments consisted of diets containing two distinct protein sources: (1) soybean meal (44 % as the control group); and (2) HI-PRO® product. Throughout the trial, measurements of nutritional digestibility and blood metabolites (total protein, albumin, urea, and creatinine) were conducted. Quantity and composition of the milk were measured to determine the content of milk proteins, lipids, and lactose. The outcome of the results showed insignificant decrease in the buffaloes receiving HI-PRO® feed versus control group. Furthermore, there was enhancement in the fiber digestibility by approximately 2.5 % in the HI-PRO® group compared to the control group. The levels of protein, albumin, globulin, urea, and creatinine fall within the normal range for animals in good health. Using HI-PRO® resulted in a marginal improvement in milk production, increasing it by approximately 4.8 % compared to soybean meal. Furthermore, the buffaloes fed HI-PRO® showed a slightly elevated 4 % fat-corrected milk output and milk composition. To summarize, nursing buffaloes can utilize HI-PRO® as an efficient protein source in their diets, replacing soybean meal.

An extended version of (3+1)-dimensional non-linear Schrödinger equation that has a cubic–quintic nonlinear component under the stochastic effects is examined in this investigation. Several stochastic exact solutions of this model is acquired through the application of the improved modified extended tanh-function scheme (IMETFS). This method offers a practical and effective approach to finding precise solutions to several kinds of nonlinear partial differential equations. In addition, these solutions include stochastic soliton solutions (bright, singular, combo dark-singular), and exact solution such as singular periodic, Jacobi elliptic function, Weierstrass elliptic doubly periodic solution, rational, and exponential functions. Since it is the first study of its sort to examine multiplicative white noise’s impacts in this particular setting, it offers fresh insights and innovative research approaches for the field’s future studies. The work adds much to our understanding of soliton theory and how it relates to optical fiber technology while illuminating hitherto unknown facets of multiplicative white noise. To illustrate the impact of the noise, a few recovered solutions with varying noise strengths are given graphically as examples.