Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method.

In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

A novel approach towards web browser using the concept of a complex spherical fuzzy soft information.

The modern technology is the practical application of scientific knowledge, whether in industry or daily life, for goals or purposes. More quickly than any other technological advancement in human history, digital technologies have advanced. The technology sector is expanding and provides both new educational opportunities and innovative, exciting products. Right now, one of the most widely used and fascinating technologies is the web browser. This article introduced the novel concepts of complex spherical fuzzy soft relations (CSFSRs) by using the Cartesian Product (CP) of two complex spherical fuzzy soft sets (CSFSSs). Additionally, examples are used to clarify various types of relations. Because it discusses all levels of membership, abstinence, and non-membership with multidimensional variables, the CSFSRs have a detailed structure. The CSFSR-based modelling tools developed in this research, which primarily rely on the score function, can be used to choose the best Web browser. The transaction could be as easy as users sharing records via a functional web browser. Finally, the advantages of this suggested structure are illustrated by contrasting it with alternative structures.

Functionalized Single Crystal Perovskite Materials for SERS and Their Potential Detection Applications.

Recent advances in detection and diagnostic tools have improved understanding and identification of plant physiological and biochemical processes. Effective and safe Surface Enhanced Raman Spectroscopy (SERS) can find objects quickly and accurately. Raman enhancement amplifies the signal by 1014-1015 to accurately quantify plant metabolites at the molecular level. This paper shows how to use functionalized perovskite substrates for SERS. These perovskite substrates have lots of surface area, intense Raman scattering, and high sensitivity and specificity. These properties eliminate sample matrix component interference. This study identified research gaps on perovskite substrates' effectiveness, precision, and efficiency in biological metabolite detection compared to conventional substrates. This article details the synthesis and use of functionalized perovskites for plant metabolites measurement. It analyzes their pros and cons in this context. The manuscript analyzes perovskite-based SERS substrates, including single-crystalline perovskites with enhanced optoelectronic properties. This manuscript aims to identify this study gap by comprehensively reviewing the literature and using it to investigate plant metabolite detection in future studies.

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique.

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

A fuel gas waste heat recovery-based multigeneration plant integrated with a LNG cold energy process, a water desalination unit, and a CO2 separation process.

Development of the multigeneration plants based on the simultaneous production of water and energy can solve many of the current problems of these two major fields. In addition, the integration of fossil power plants with waste heat recovery processes in order to prevent the release of pollutants in the environment can simultaneously cover the environmental and thermodynamic improvements. Besides, the addition of a carbon dioxide (CO2) capturing cycles with such plants is a key issue towards a sustainable environment. Accordingly, a novel waste heat recovery-based multigeneration plant integrated with a carbon dioxide separation/liquefaction cycle is proposed and investigated under multi-variable assessments (energy/exergy, financial, and environmental). The offered multigeneration system is able to generate various beneficial outputs (electricity, liquefied CO2 (L-CO2), natural gas (NG), and freshwater). In the offered system, the liquified natural gas (LNG) cold energy is used to carry out condensation processes, which is a relatively new idea. Based on the results, the outputs rates of net power, NG, L-CO2, and water were determined to be approximately 42.72 MW and 18.01E+03, 612 and 3.56E+03 kmol/h, respectively. Moreover, the multigeneration plant was efficient about 32.08% and 87.72%, respectively, in terms of energy and exergy. Economic estimates indicated that the unit product costs of electricity and liquefied carbon dioxide production, respectively, were around 0.0466 USD per kWh and 0.0728 USD per kg-CO2. Finally, the total released CO2 was about 0.034 kg per kWh. According to a comprehensive comparison, the offered multigeneration plant can provide superior environmental, thermodynamic, and economic performances compared to similar plants. Moreover, there was no need to purchase electricity from the grid.

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis.

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system's solutions, we investigate stochasticity's influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

Advancing COVID-19 stochastic modeling: a comprehensive examination integrating vaccination classes through higher-order spectral scheme analysis.

This research article presents a comprehensive analysis aimed at enhancing the stochastic modeling of COVID-19 dynamics by incorporating vaccination classes through a higher-order spectral scheme. The ongoing COVID-19 pandemic has underscored the critical need for accurate and adaptable modeling techniques to inform public health interventions. In this study, we introduce a novel approach that integrates various vaccination classes into a stochastic model to provide a more nuanced understanding of disease transmission dynamics. We employ a higher-order spectral scheme to capture complex interactions between different population groups, vaccination statuses, and disease parameters. Our analysis not only enhances the predictive accuracy of COVID-19 modeling but also facilitates the exploration of various vaccination strategies and their impact on disease control. The findings of this study hold significant implications for optimizing vaccination campaigns and guiding policy decisions in the ongoing battle against the COVID-19 pandemic.

Salmonella meningitis in a young child from Pakistan: a case report.

BACKGROUND: Salmonella meningitis is a rare but serious complication of Salmonella infection, primarily affecting infants, children, and immunocompromised individuals. CASE PRESENTATION: We present a case of a two-and-a-half-year-old Asian boy who developed Salmonella meningitis along with pneumonia and respiratory failure. Initially, he experienced symptoms of loose motions, fever, and irritability, which progressed to neck stiffness and brisk reflexes. Cerebrospinal fluid (CSF) analysis confirmed Salmonella typhi in the CSF. Due to the worsening condition, the patient was admitted to the intensive care unit, intubated, and switched to meropenem as the antibiotic of choice after an initial empiric therapy with ceftriaxone and vancomycin. With appropriate treatment, the patient showed significant improvement, including resolution of fever and respiratory symptoms. CONCLUSION: Management of Salmonella meningitis is often challenging primarily because of the fact that the empiric therapy for meningitis may not always provide coverage to the multi-drug resistant Salmonella species found in South Asia. Prompt administration of appropriate antibiotics based on sensitivity testing is crucial for successful management. This case emphasizes the importance of early recognition and effective management of this uncommon yet severe complication of Salmonella infection.

Spatial spillover impact of determinants on child mortality in Pakistan: evidence from Spatial Durbin Model.

BACKGROUND: Child mortality is a major challenge to public health in Pakistan and other developing countries. Reduction of the child mortality rate would improve public health and enhance human well-being and prosperity. This study recognizes the spatial clusters of child mortality across districts of Pakistan and identifies the direct and spatial spillover effects of determinants on the Child Mortality Rate (CMR). METHOD: Data of the multiple indicators cluster survey (MICS) conducted by the United Nations International Children's Emergency Fund (UNICEF) was used to study the CMR. We used spatial univariate autocorrelation to test the spatial dependence between contiguous districts concerning CMR. We also applied the Spatial Durbin Model (SDM) to measure the spatial spillover effects of factors on CMR. RESULTS: The study results showed 31% significant spatial association across the districts and identified a cluster of hot spots characterized by the high-high CMR in the districts of Punjab province. The empirical analysis of the SDM confirmed that the direct and spatial spillover effect of the poorest wealth quintile and MPI vulnerability on CMR is positive whereas access to postnatal care to the newly born child and improved drinking water has negatively (directly and indirectly) determined the CMR in Pakistan. CONCLUSION: The instant results concluded that spatial dependence and significant spatial spillover effects concerning CMR exist across districts. Prioritization of the hot spot districts characterized by higher CMR can significantly reduce the CMR with improvement in financial statuses of households from the poorest quintile and MPI vulnerability as well as improvement in accessibility to postnatal care services and safe drinking water.

Thermal and physical impact of viscoplastic nanoparticles in a complex divergent channel due to peristalsis phenomenon: Heat generation and multiple slip effects.

In the advance studies, researchers have performed productive research contributions in the field of nanofluid mechanics under various biological assumptions. These contributions are fruitful to understand the applications of nanofluids in the various fields such as hybrid-powered engine, heart-diagnose, to prevent numerous diseases, heat exchanger, pharmaceutical processes, etc. The current analysis explores the combined effects of heat generation and chemical reaction on the peristaltic flow of viscoplastic nanofluid through a non-uniform (divergent) channel. The physical effects of second-order velocity slip, thermal slip and mass slip parameters on the rheological characteristics are also considered. To describe non-Newtonian effects, the Casson fluid is deployed. The greater wavelength assumption and low Reynolds number theory are used to attain the rheological equations. Numerical solutions of these governing equations associated with suitable boundary conditions are obtained via Mathematica symbolic software. The velocity magnitude of Casson fluid is higher than associated with Newtonian fluid. Radiation parameter has a vigorous impact in the reduction (enhancement) of temperature (mass concentration) profile. The porous parameter has a remarkable impact in reduction of temperature and velocity profile. Thermal enhancement is perceived by intensifying the chemical reaction parameter, and opposite inclination is noticed in mass concentration. Temperature has been demonstrated to be increased by increasing the Darcy number. The magnitudes of both axial velocity and temperature distribution are smaller in the presence of second-order velocity slip parameters effect as compared with no-slip condition. The magnitudes of axial velocity and mass (or, nanoparticle) concentration are augmented by accumulating the Prandtl number. A rise in Brownian parameter is noticed to depress the mass concentration. The present study has been used in bio-mechanical processes, nanomaterial devices, heat transfer enhancement, radiators, and electronics cooling systems.

Entropy optimized flow of Sutterby nanomaterial subject to porous medium: Buongiorno nanofluid model.

Owing to enhanced thermal impact of nanomaterials, different applications are suggested in engineering and industrial systems like heat transfer devices, energy generation, extrusion processes, engine cooling, thermal systems, heat exchanger, chemical processes, manufacturing systems, hybrid-powered plants etc. The current communication concerns the optimized flow of Sutterby nanofluid due to stretched surface in view of different thermal sources. The investigation is supported with the applications of external heat source, magnetic force and radiative phenomenon. The irreversibility investigation is deliberated with implementation of thermodynamics second law. The thermophoresis and random movement characteristics are also studied. Additionally, first order binary reaction is also examined. The nonlinear system of the governing problem is obtained which are numerically computed by s method. The physical aspects of prominent flow parameters are attributed graphically. Further, the analysis for entropy generation and Bejan number is focused. It is observed that the velocity profile increases due to Reynolds number and Deborah number. Larger Schmidt number reduces the concentration distribution. Further, the entropy generation is improved against Reynolds number and Brinkman parameter.

Thermal inspection for viscous dissipation slip flow of hybrid nanofluid (TiO2-Al2O3/C2H6O2) using cylinder, platelet and blade shape features.

Hybrid nanofluid are the modified class of nanofluids with extra high thermal performances and present different applications in automotive cooling, heat transfer devices, solar collectors, engine applications, fusion processes, machine cutting, chemical processes etc. This thermal research explores the heat transfer assessment due to hybrid nanofluid with of different shape features. The thermal inspections regarding the hybrid nanofluid model are justified with aluminium oxide and titanium nanoparticles. The base liquid properties are disclosed with ethylene glycol material. The novel impact of current model is the presentation of different shape features namely Platelets, blade and cylinder. Different thermal properties of utilized nanoparticles at various flow constraints are reported. The problem of hybrid nanofluid model is modified in view of slip mechanism, magnetic force and viscous dissipation. The heat transfer observations for decomposition of TiO2-Al2O3/C2H6O2 is assessed by using the convective boundary conditions. The shooting methodology is involved for finding the numerical observations of problem. Graphical impact of thermal parameters is observed for TiO2-Al2O3/C2H6O2 hybrid decomposition. The pronounced observations reveal that thermal rate enhanced for blade shaped titanium oxide-ethylene glycol decomposition. The wall shear force reduces for blade shaped titanium oxide nanoparticles.

Free convective oscillatory flow due to inclined perpendicular shield subject to the thermos-diffusion and suction effects.

An unsteady free convective flow of an electrically conducting viscous fluid due to accelerated inestimable inclined perpendicular shield has been presented in presence of heat and mass transfer phenomenon. The applications of thermos-diffusion and heat source are also incorporated. The chemical reaction consequences are considered in the concentration equation. The compelling meadow is considered to be homogeneous and practical perpendicular to the flow direction. Further, the oscillatory suction effects are also taken into observations for porous regime. The closed form expressions are resulted with implementation of perturbation approach. The non-dimensional expression for the proposed governing system is yield out with entertaining appropriate variables. The graphically influence of parameters is studied. Following to obtained observations, it is claimed that declining deviation in velocity is predicted with chemical reactive factor. Further, less thermal transport between container to fluid is noticed for radiative absorption parameter.

On the Bioconvective Aspect of Viscoelastic Micropolar Nanofluid Referring to Variable Thermal Conductivity and Thermo-Diffusion Characteristics.

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters' effects are computationally evaluated for some definite range.

Mathematical analysis of COVID-19 pandemic by using the concept of SIR model.

The health organizations around the world are currently facing one of the greatest challenges, to overcome the current global pandemic, COVID-19. It erupted in December 2019, in Wuhan City, China. It spreads rapidly throughout the world within couple of months. In this paper, the data of the COVID-19 have been collected, organized, analyzed and interpreted using the discrete-time model of SIR epidemic model. Moreover, results for several countries from different regions of the world have been obtained. Furthermore, comparative study has been carried out for the countries under consideration. The comparison was performed for the data of different countries on same dates of each month. However, the calculations are carried out for thirteen consecutive weeks, to investigate the rate of spread and the control of the disease in these countries. This guides us to some important concepts like factors favoring the spread of virus and those resisting the spread. Different regions are studied and their data have been evaluated to know which regions are the most effected. This study helps to know the important factors about the behavior of the coronavirus in different environments, such as lockdowns, temperatures, humidity and other restrictions. The proposed concepts and equations can be used to project the upcoming behavior of the pandemic.

Thermal transport of biological base fluid with copper and iron oxide nanoparticles in wavy channel.

The nanoparticles are frequently used in biomedical science for the treatment of diseases like cancer and these nanoparticles are injected in blood which is transported in the cardiovascular system on the principle of peristalsis. This study elaborates the effects of Lorentz force and joule heating on the peristaltic flow of copper and iron oxide suspended blood based nanofluid in a complex wavy non-uniform curved channel. The Brinkman model is utilized for the temperature dependent viscosity and thermal conductivity. The problem is formulated using the fundamental laws in terms of coupled partial differential equations which are simplified using the creeping flow phenomenon. The graphical results for velocity, temperature, streamlines, and axial pressure are simulated numerically. The concluded observations deduce that the solid volume fraction of nanoparticles reduces the velocity and enhance the pressure gradient and accumulation of trapping bolus in the upper half of the curved channel is noticed for temperature dependent viscosity.

The minimality of mean square error in chirp approximation using fractional fourier series and fractional fourier transform.

Chirps are familiar in nature, have a built-in resistance to noise and interference, and are connected to a wide range of highly oscillatory processes. Detecting chirp oscillating patterns by traditional Fourier series is challenging because the chirp frequencies constantly change over time. Estimating such types of functions considering the partial sums of a Fourier series in Fourier analysis does not permit an approximate solution, which entails more Fourier coefficients required for signal reconstruction. The standard Fourier series, therefore, has a poor convergence rate and is an inadequate approximation. In this study, we use a parameterized orthonormal basis with an adjustable parameter to match the oscillating behavior of the chirp to approximate linear chirps using the partial sums of a generalized Fourier series known as fractional Fourier series, which gives the best approximation with only a small number of fractional Fourier coefficients. We used the fractional Fourier transform to compute the fractional Fourier coefficients at sample points. Additionally, we discover that the fractional parameter has the best value at which fractional Fourier coefficients of zero degrees have the most considerable magnitude, leading to the rapid decline of fractional Fourier coefficients of high degrees. Furthermore, fractional Fourier series approximation with optimal fractional parameters provides the minimum mean square error over the fractional Fourier parameter domain.

Nonlinear Thermal Diffusion and Radiative Stagnation Point Flow of Nanofluid with Viscous Dissipation and Slip Constrains: Keller Box Framework Applications to Micromachines.

The radiated flow of magnetized viscous fluid subject to the viscous dissipation phenomenon is numerically studied. The radiative phenomenon is addressed with nonlinear relations. Further, analysis is performed by using the slip effects and convective thermal flow constraints. The transformed problem is numerically evaluated using the Keller Box method. The physical parameter effects, such as the magnetic parameter for the velocity profile, Prandtl number, Brownian motion parameter and Biot number for the energy profile and Lewis number, and the thermophoresis parameter for the concentration profile are discussed. The obtained results suggest applications in enhancing the heat transfer phenomenon, thermal system, energy generation, heat transmission devices, power generation, chemical reactions, etc.

Peristaltic Phenomenon in an Asymmetric Channel Subject to Inclined Magnetic Force and Porous Space.

This research is engaged to explore biological peristaltic transport under the action of an externally applied magnetic field passing through an asymmetric channel which is saturated with porous media. The set of governing partial differential equations for the present peristaltic flow are solved in the absence of a low Reynolds number and long wavelength assumptions. The governing equations are to be solved completely, so that inertial effects can be studied. The numerical simulations and results are obtained by the help of a finite element method based on quadratic six-noded triangular elements equipped with a Galerkin residual procedure. The inertial effects and effects of other pertinent parameters are discussed by plotting graphs based on a finite element (FEM) solution. Trapped bolus is discussed using the graphs of streamlines. The obtained results are also compared with the results given in the literature which are highly convergent. It is concluded that velocity and the number of boluses is enhanced by an increase in Hartmann number and porosity parameter K Increasing inertial forces increase the velocity of flow but increasing values of the porosity parameter lead to a decrease in the pressure gradient. The study elaborates that magnetic field and porosity are useful tools to control the velocity, pressure, and boluses in the peristaltic flow pattern.

Modeling and Mathematical Investigation of Blood-Based Flow of Compressible Rate Type Fluid with Compressibility Effects in a Microchannel.

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress-strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and Dwall increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid.