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In this article, a photovoltaic thermal (PV/T) system is optimized using hybrid nanofluids composed of copper and aluminum oxide, with water as the base fluid for cooling applications. The PV/T system features a simple configuration, with mono-crystalline silicon above the flow channel, copper functioning as the absorber, and a trapezoidal-shaped flow channel. The inlet height of the flow channel is fixed, while the outlet height is variable, defining an aspect ratio that ranges from 0.4 to 1. Numerical modeling is carried out using COMSOL Multiphysics 6.0 through the finite element method, applying the two-dimensional incompressible Navier-Stokes and energy equations. The study focuses on analyzing cell temperature and electrical efficiency using both qualitative and quantitative approaches by varying the Reynolds number, aspect ratio, inlet temperature, and volume fraction of the hybrid nanofluids.Key findings: The results demonstrated a significant 37 % reduction in cell temperature as the Reynolds number increased from 100 to 400, and a 1.8 % reduction when the aspect ratio was minimized to 0.4. Additionally, cell efficiency improved by 8.4 % and 2.1 % as the Reynolds number increased from 100 to 1000 and the volume fraction from 0.01 to 0.1, respectively. These findings provide effective strategies for enhancing the electrical efficiency of PV/T systems. ''The study suggests optimizing the cell efficiency of PV/T systems through a new configuration of the flow channel, focusing on adjusting the outlet height and the concentration of nanoparticles in the base fluid.

In this article, we propose a novel new iteration method and homotopy perturbation method (HPM) along with the Elzaki transform to compute the analytical and semi-analytical approximations of fractional Airy’s-type partial differential equations (FAPDEs) subjected to specific initial conditions. A convergent series solution form with easily commutable coefficients is used to examine and compare the performance of the suggested methods. Using Maple graphical method analysis, the behavior of the estimated series results at various fractional orders ς\varsigma and its modeling in two-dimensional (2D) and three-dimensional (3D) spaces are compared with actual results. Also, detailed descriptions of the physical and geometric implications of the calculated graphs in 2D and 3D spaces are provided. As a result, the obtained solutions of FAPDEs that are subject to particular initial values quite closely match the exact solutions. In this way, to solve FAPDEs quickly, the proposed approaches are considered to be more accurate and efficient.

In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains.

The aim of this article is to present a comparison of two analytical approaches toward obtaining the solution of the time-fractional system of partial differential equations. The newly proposed approaches are the new approximate analytical approach (NAAA) and Mohand variational iteration transform approach (MVITA). The NAAA is based on the Caputo-Riemann operator and its basic properties with the decomposition procedure. The NAAA provides step wise series form solutions with fractional order, which quickly converge to the exact solution for integer order. The MVITA is based on a variational iteration procedure and uses the Mohand integral transform. The MVITA also provides a series solution without a stepwise solution. Both approaches provide a series form of solutions to the proposed problems. The analytical procedures and obtained results are compared for the proposed problems. The obtained results were also compared with exact solutions for the problems. The obtained result and plots have shown the validity and applicability of the proposed algorithms. Both approaches can be extended for the analytical solution of other physical phenomena in science and technology.

In this paper, we have studied a three-dimensional model to describe the behavior of tumor cells in the absence of the immune response, which is composed of tumor, normal and fat cells (TNF) under time delay effect. The center manifold theory has been used to study the bifurcation behavior. It is proven that TNF model undergoes codimension-1 bifurcation, while Hopf bifurcation does not occur in the non-delay model. For delayed TNF, we take into the late response of fat cells to tumor cells. Consequently, the delay factor is a considerable parameter in TNF model. Hence, we presented a formula of the time delay value for the occurrence of periodic solutions. Additionally, the stability of Hopf bifurcation was analysed. Numerical simulations are provided to illustrate and extend the theoretical results, we provide our study with numerical simulations inclusive families of periodic solutions.

In this research study, we focus on the generalized regularized long wave equation and the modified regularized long wave equation, which play pivotal roles in characterizing plasma waves in oceans and ion acoustic waves in shallow water, a domain deeply rooted in physical phenomena. Employing two computational techniques, namely, the optimal auxiliary function method and the Laplace iterative transform method, we approximate these equations. These formulas are used to characterize plasma waves in oceans and ion acoustic waves in shallow water. The results discovered have important ramifications for our comprehension of many physical events. Our results show that both methods are robust, easy to use, and successful. Both methods yield results that are satisfactory to each other. With the use of tables and graphs, we compared the two suggested approaches. The findings suggest that the suggested methods can be widely applied to explore other real-world problems.

In this article, the solutions of higher nonlinear partial differential equations (PDEs) with the Caputo operator are presented. The fractional PDEs are modern tools to model various phenomena more accurately. The residual power series method (RPSM) is used for the solution analysis of fractional partial differential equations (FPDEs), which has direct implementation for the solutions of fractional partial differential equations. In this work, the solutions to a few nonlinear FPDEs are handled by the proposed technique. The general and particular schemes of RPSM are constructed and implemented successfully. The fractional solutions of PDEs have provided many useful dynamics of the targeted problems. The RPSM results for both integer and fractional-order FPDEs are further explained and elaborated by using graphs and tables. It is observed that the higher accuracy of RPSM is achieved with fewer calculations. Graphs and tables for fractional-order solutions are presented, which confirm the convergence phenomena of fractional solutions toward integer order solutions of each problem. The suggested method can be extended to the solutions of other nonlinear fractional partial differential equations.

The “hard water” factor shows the management of water in the Nusa Tenggara Timur, which shows a higher ratio based on the ion’s minerals. The incessant use of hard water presents kidney dysfunction, which produces diabetic and vascular kinds of diseases. Therefore, it is essential to recognize the influences of hard water on kidney function. A novel design of a stochastic solver using the transfer radial basis function is provided by applying the Bayesian regularization neural network for solving the model. The kidney dysfunction mathematical system is divided into humans (susceptible, infected, recovered) and water components (magnesium, calcium). Twelve numbers of neurons with the radial basis transfer function have been used in the hidden layers for solving the model. The approach performance is remarked through the results comparison and further reducible absolute error found around 10−06 to 10−08 develop the scheme’s exactness. Moreover, the statistical performances including regression coefficient performances around 1 for each case of the model validate the reliability and exactness of the scheme for solving the model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.

The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.

In this paper, we aim to propose a novel q-fractional derivative in the Caputo sense included proportional derivative. To this end, we firstly introduced a new concept of proportional q-derivative and discussed its properties in detail. Then, we add this definition in the concept of Caputo derivative to state a new type of dynamical system with q-calculus. For analytically solving this system, q-Laplace transform has been successfully applied to obtain the solutions. Indeed, the bivariate Mittag-Leffler function has an essential role in this regard. Two illustrative examples are also given in detail.

Theoretically, this work describes the exact solutions of fractional Casson fluid through a channel under the effect of MHD and porous medium. The unsteady fluid motion of the bottom plate, which is confined by parallel but perpendicular sidewalls, supports the flow. By introducing the dimensionless parameters and variables, the momentum equation, as well as the initial and boundary conditions, has been transformed to a dimensionless form. A mix of Laplace and Fourier transformations is used to get the exact solution for the momentum equation. The constitutive equations for Caputo-Fabrizio’s time-fractional derivative are also incorporated for recovering the exact solutions of the flow problem under consideration. After recovering the exact solutions for flow characteristics, three different cases at the surface of the bottom plate are discussed, by addressing the limiting cases under the influence of the side walls. Moreover, these solutions are captured graphically, and the effects of the Reynolds number Re, fractional parameter α, effective permeability Keff, and dimensionless parameter for Casson fluid β on the fluid’s motion are observed.

This paper shows the outcomes of computer virus propagation (CVP) model, represented with susceptible, exposed, infected, quarantine and recovered computers (SEIRQ), classes based mathematical model using the stochastic procedures. The systematic study of the CVP based SEIRQ model represents that the equilibrium state of virus-free is stable globally with reproduction not more than one, while the viral symmetry is attractive globally. The numerical performances of the CVP based SEIRQ model are presented by using the stochastic computational framework based on the artificial neural networks (ANNs) together with the Levenberg-Marquardt backpropagation (LBMB) called as ANNs-LBMB. The learning procedures via ANNs-LBMB for solving the CVP based SEIRQ model are implemented to indorse the statics using the testing, authorization, and training. Thirteen numbers of neurons and the data selection for training 72%, testing 12% and validation 16% are selected to solve the model. For the numerical outcomes of the CVP based SEIRQ model using the ANNs-LBMB, a dataset is considered through the Adams approach. The accuracy and reliability performances of the scheme are presented by using the values of the absolute error (AE) along with the observations of state transitions (STs), regression, mean square error (MSE) and error histograms (EHs). [ABSTRACT FROM AUTHOR]

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas. [ABSTRACT FROM AUTHOR]

This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.