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The generated nonlocal correlations of two superconducting-charge (SCC) qubits including uncertainty-induced nonlocality (UIN), Bell-Horodecki nonlocality, and negativity’s entanglement have been explored by intrinsic decoherence model. An initial separable two SCC-qubits state to study the generation of nonlocal correlations. By adjusting the intrinsic decoherence intensity and the two superconducting-qubits interaction parameters (of Josephson energies, the mutual two SCC-qubits coupling energy, and the difference between the Josephson SCC-qubit energies), we can control the produced maximum Bell-Horodecki nonlocality, UIN, and entanglement, which their dynamics align with the hierarchy principle. It is found that the generations of two-qubit states, having Bell-Horodecki nonlocality, UIN, and negativity entanglement, by the interactions of two SCC-qubits depend on their interaction parameters and intrinsic decoherence. For weak mutual two SCC-qubits coupling energy and the Josephson SCC-qubit energies with a slight difference between the Josephson SCC-qubit energies, the generated two SCC-qubit state has strong nonlocal correlation dynamics. The mutual coupling energy for two SCC-qubits can enhance the generation of weak nonlocal correlation dynamics when there is a significant difference between the Josephson SCC-qubit energies. Controlling Josephson energy, mutual coupling, and the energy difference of SCC-qubits can improve nonlocal correlations’ robustness against intrinsic decoherence.

The increasing demand for thermal management due to the high heat density heat exchangers for different technological and industrial processes draw the attention of researchers in heat transfer analysis to investigate the simultaneous solution to this problem. Keeping this in mind, the current work addressed the utilization of ternary hybrid nanofluid, a mixture of graphene oxide with silver and copper, to examine the heat and mass transfer enhancement of MHD Maxwell fluid. In the current model, the author discussed heat and mass transfer analysis of Maxwell MHD ternary hybrid nanofluid flow across a porous medium over an extending sheet. The energy and concentration equations are expressed to include the effects of Brownian motion and thermophoretic diffusion. Additionally, the effects of thermal radiation, activation energy, chemical reactions, and convective boundary conditions are considered. The similarity transformations are used to convert the nonlinear PDEs into ODEs. The impact of embedded factors on velocity, temperature, and concentration profiles is perceived graphically and mathematically by using the HAM technique. The convergence of computed solutions is ensured by h-curves. The significant outcomes from the analysis expressed that the flow distribution increases with slip and suction/injection factors. The concentration of the ternary hybrid nanofluid increases with an increase in thermophoretic diffusion (0.1–0.5), thermal biot number, and solutal biot number (0.1–0.5), however, a declining behavior is perceived with rising quantity of Schmidt number (0.6–0.8) and Brownian motion (0.1–0.5) parameters. Nusselt number shows a dominant behaviour with a higher magnetic factor. Similarly, the skin friction increases with an increase in thermal biot number and thermophoresis factor. It is revealed that the skin friction along x− direction increases from (0.78138, 0.833702, 0.897022, and 0.972526) for ternary hybrid nanofluid. Nusselt number increases from 2 to 5% (0.208936, 0.214288, 0.219799, 0.22555) when the volume fraction varies from 0.01 to 0.04 respectively.

Hepatitis B virus (HBV) is a much more threatening and prolonged disease than hepatitis A. It can start as an acute disease, but in roughly 5 to 10% of situations, it can progress to a chronic condition that permanently damages the liver. After getting or coming into contact with the Hepatitis B virus (HBV), the said symptoms normally last from 10 days to 6 months. In the present paper, to have a firm understanding of the dynamics of HBV, we derived a new fractional model in the Caputo sense with asymptomatic carriers, vaccination, and treatment classes. We obtain the basic reproduction number R0 for the diagnosis and recurrence of the disease. We determine the stability of the proposed model locally and globally for R0 values less than and greater than 1. We use the Lyapunov function theory in fractional environments to establish the global stability of the fractional Hepatitis B virus (HBV) model. We demonstrate the existence and uniqueness of the fractional-order model. To look at the fractional order model’s solution graphically, we used a useful numerical strategy to get more detailed numerical results for the factors that have a big effect on getting rid of diseases. Additionally, the inclusion of the treatment class in the population allows for the determination of the impact of alternative medicines used to treat infected populations. Numerical simulation of the proposed fractional order (FO) Caputo model is performed, allowing for the analysis of graphical representations and the significance of fractional order derivatives to illustrate the impact of our theoretical findings.

Abstract The control and management of energy and their associated issues are increasingly recognized as one of mankind’s greatest challenges in the coming years to keep pace with the surge in industrialization and technology. Free convection optimizes the heat transfer processes in energy systems like solar collectors and power plants, reducing energy consumption and increasing system effectiveness. Further, studying and analyzing critical factors like magnetic fields, thermal radiation, and the shape of nanoparticles can assist in the control of fluid motion and improve the efficiency of heat transfer processes in a wide range of real-world applications, such as the power sector, aerospace applications, molten metal, nuclear power, and aeronautical engineering. This study aims to scrutinize the thermal performance of a magneto tri-hybrid polar nanoliquid flowing over a radiative sphere, considering the nanosolids’ shape. The single-phase model is developed to acquire the problems governing equations, and the hybrid linearization spectral collection approach is utilized to approximate the solution. The present findings reveal that blade-shaped nanosolids exhibit the highest thermal conductivity ratio when incorporated into the base fluid, whereas spherical nanosolids exhibit the lowest ratio. Volume fraction and thermal radiation factors have an effective role in raising fluid velocity and thermal performance. The magnetic and microapolar factors significantly suppress fluid velocity and energy transfer. As the volume fraction factor increases, the average percentage improvement in convective heat transfer for Al2O3 + Cu + MWCNT/kerosene oil compared to Al2O3 + Cu + graphene/kerosene oil approximately ranges from 0.8 to 2.6%.

Researchers are paying close attention to Casson fluid due to their noteworthy applications in industries. Among the non-Newtonian substances, the Casson fluid is one of the most important types. In this paper, the flow of sodium alginate-based Casson hybrid nanofluid flow mixed with copper and alumina nanoparticles across a stretching sheet is investigated. The slips and convective boundary conditions are assumed in the problem. Moreover, the flow of the hybrid nanofluid is magnetically influenced. Additionally, the consequences of viscous dissipation are considered. Through similarity variables, the leading nonlinear PDEs are converted into ODEs, which are then simplified by the homotopy analysis method (HAM). The variations in velocities, temperature, skin friction, and Nusselt number are exhibited in the figures. With the help of figures, the convergence analysis of the present model has been shown. The result reveals that the Casson factor has a declining consequence on the velocity profile along the x − direction and y − directions. An improvement behavior is observed in the velocity plot in the y − direction through the stretching ratio parameter. The Casson parameter has a declining effect on the velocity profile along x-direction and ydirections. It is noticed that the temperature plot shows an escalating behavior through the Eckert number and magnetic parameter. From the numerical result, it is concluded that the Skin friction and Nusselt number of hybrid nanofluid is maximum as compared to nanofluid.

The use of fractal–fractional derivatives has attracted considerable interest in the analysis of chaotic and nonlinear systems as they provide a unique capability to represent complex dynamics that cannot be fully described by integer-order derivatives. The fractal–fractional derivative with a power law kernel is used in this paper as an analytical tool to analyze the dynamics of a chaotic integrated circuit. Using coupled ordinary differential equations of classical order, the complexity of an integrated circuit is modeled. The classical order model is generalized via fractal–fractional derivatives of the power law kernel. Moreover, this paper is concerned with investigating the Ulam stability of the model and conducting theoretical studies in order to analyze equilibrium points, identify unique solutions, and verify the existence of such solutions. By examining the complex dynamics that result in chaotic behavior, these investigations shed light on the fundamental properties of integrated circuits. For the purpose of exploring the non-linear fractal–fractional order system, a numerical algorithm has been developed to facilitate our analysis. MATLAB software has been used to implement this algorithm, making it possible to carry out detailed simulations. Simulating solutions are accomplished using 2D and 3D portraits, which provide visual and graphical representations of the results. Throughout the simulation phase, particular attention is given to the impact of fractional order parameter and fractal dimension. As a result of this study, we have gained a comprehensive understanding of the behavior of the system and its response to variations in values.

It is essential for mathematicians, physicists, and engineers to construct fractional mathematical models for specific phenomena and develop numerical or analytical solutions for these models. In this work, we implement the natural decomposition approach with nonsingular kernel derivatives to investigate the solution of nonlinear fractional forced Korteweg–de Vries (FF-KdV) equation. We first investigate the FF-KdV equation under the Caputo–Fabrizio fractional derivative. The similar equations are then examined using the Atangana–Baleanu derivative. This approach combines the decomposition method with the Natural transform method. The series solution of the suggested equations is thus obtained using the natural transform. The key benefit of this novel approximate-analytical approach is that it may provide an analytical solution for the FF-KdV problem in the form of convergent series with simple computations. For each equation, three unique situations are chosen to demonstrate and test the viability of the proposed method. To guarantee the competence and dependability of the proposed method, the nature for various values of the Froude number Fr have been provided. The present approach is also used to calculate solutions at various fractional orders. The approximate series solution’s behavior for various fractional orders has been graphically displayed. The outcomes demonstrate that the methodology is simple to use and reliable when applied to numerous fractional differential equations.

The current research focuses on harnessing the computational power of neural networks, notably the Levenberg-Marquardt backpropagation optimization algorithm (ANN-LMBOA), to simulate the behavior of magnetohydrodynamic (MHD) three-dimensional non-Newtonian Darcy-Forchheimer flow of Casson nanofluid over a stretching surface situated within a porous medium. The fluid flow is subject to the influence of Hall and ion slip forces, contributing to its behavior. Additionally, the Cattaneo–Christov heat flux model is incorporated to represent the temperature balance in the boundary layer accurately. Non-Newtonian fluids improve thermal transmission due to their shear-thinning propensity, increased turbulence, and more excellent convective heat transfer. The thermal conductivity of nanofluids is increased by the inclusion of nanoparticles, enabling more effective heat transmission. Buongiorno's model is used for the nanofluid phenomena that concentrate on thermophoresis and Brownian motion. To tackle the flow problem efficiently, the governing equations are transformed into non-linear differential equations using self-similar variables. The ANN-LMBOA algorithm is then employed to solve these equations, providing a practical and accurate approach to the simulation. To train and validate the ANN-LMBOA model, a dataset is generated using the bvp4c numerical method, which can easily handle highly non-linear coupled differential equations. The dataset is created for different scenarios of flow parameters, facilitating comprehensive training, testing, and authentication of the neural network. The accuracy of the ANN-LMBOA model is assessed through various statistical neural network tools, such as MSE, RP, CF graphs, and EH. The study thoroughly investigates flow model parameters related to momentum, energy, and concentration profiles, which are presented using visual representations to understand the system's behavior and characteristics comprehensively. The effects of various parameters of interest like Casson, ion slip, porosity, thermal relaxation, and magnetic parameters on velocity, temperature, and concentration distribution have been studied numerically via ANN-LMBOA networks. The absolute error of reference and target data is obtained in the range of 10−4 − 10−5which proves the best accuracy performance of ANN-LMBOA networks. By raising the Prandtl and Schmidt numbers, solutal, thermal, and diffusional variables, one can reduce the diffusion of mass and heat.

This paper concerns multivariate machine learning-based prediction models of freeway traffic flow under non-recurrent events. Five model architectures based on the multi-layer perceptron (MLP), convolutional neural network (CNN), long short-term memory (LSTM), CNN-LSTM and Autoencoder LSTM networks have been developed to predict traffic flow under a road crash and the rain. Using an input dataset with five features (the flow rate, the speed, and the density, road incident and rainfall) and two standard metrics (the Root Mean Square error and the Mean Absolute error), models’ performance is evaluated.

In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He’s polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study’s findings as a tool.