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Infectious disease cryptosporidiosis is caused by the cryptosporidium parasite, a type of parasitic organism. It is spread through the ingestion of contaminated water, food, or fecal matter from infected animals or humans. The control becomes difficult because the parasite may remain in the environment for a long period. In this work, we constructed an epidemic model for the infection of cryptosporidiosis in a fractional framework with strong and weak immunity concepts. In our analysis, we utilize the well-known next-generation matrix technique to evaluate the reproduction number of the recommended model, indicated by R0. As R0<1 , our results show that the disease-free steady-state is locally asymptotically stable; in other cases, it becomes unstable. Our emphasis is on the dynamical behavior and the qualitative analysis of cryptosporidiosis. Moreover, the fixed point theorem of Schaefer and Banach has been utilized to investigate the existence and uniqueness of the solution. We identify suitable conditions for the Ulam-Hyers stability of the proposed model of the parasitic infection. The impact of the determinants on the sickness caused by cryptosporidiosis is highlighted by the examination of the solution pathways using a novel numerical technique. Numerical investigation is conducted on the solution pathways of the system while varying various input factors. Policymakers and health officials are informed of the crucial factors pertaining to the infection system to aid in its control. [ABSTRACT FROM AUTHOR]

We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up. [ABSTRACT FROM AUTHOR]

It is observed that the exposure to environmental factors such as indoors and outdoors air pollution, cigarette smoke, and allergens are highly related to asthma attacks. It is also reported that limited exposure to asthma riggers, cure due to medicine, the attacks of asthma can be minimized. In this paper, we formulate the dynamics of asthma with smoking and environmental factors classes in the fractional Caputo-Fabrizio (CF) framework to visualize its dynamical behaviour. We delineate the important properties of the CF derivative for the analysis of our model. The model is then analyzed for the basic properties and the uniqueness and existence of the hypothesized asthma system are investigated via the theory of fixed point. Furthermore, a novel numerical scheme is presented for the solution of our fractional system to illustrate the time series of asthma model. The dynamical behaviour of our asthma model is then highlighted numerically to show the impact of fractional-order ϧ on the system and to visualize the role of input factors on the dynamics of asthma disease. [ABSTRACT FROM AUTHOR]

It is acknowledged that dengue infection has a significant economic impact due to healthcare costs and lost productivity. Research can provide insights into the economic burden of the disease, guiding policymakers in their allocation of resources for prevention and control interventions. In this work, we structured a novel mathematical model that describes the spread of dengue with the effects of carriers, an index of memory and vaccination. To show the effect of treatment on the dynamics of dengue, we have incorporated medication-related treatment into the system. The proposed dynamics are represented by using fractional derivatives to capture the role of memory in the control of the infection. We introduced the fundamental principles and notions of non-integer derivatives for the analysis of the model; moreover, the existence and uniqueness results for the solution of the system have been established with the help of mathematical skills. The theory of fixed points has been utilized for the analysis and examination of the system. We have established Ulam-Hyers stability for the recommended system of dengue infection. Regarding the numerical findings, a numerical method is presented to highlight the solution pathways for the system of dengue infection. Several simulations have been performed to visualize the contribution of the input parameters of the system to the prevention and control of the infection. The index of memory, vaccination, and treatment are suggested to be attractive parameters which can reduce the level of infection while the biting rate, asymptomatic carriers and transmission rate are critical as they can increase the risk of the infection in society. Our findings not only provide information for the effective management of the infection they also possess valuable insights that can improve public health. [ABSTRACT FROM AUTHOR]

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam–Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables. [ABSTRACT FROM AUTHOR]

In this study, we formulate a mathematical model in the framework of the Atangana-Baleanu fractional derivative in Caputo sense to study the transmission of tungiasis. In this formulation, interactions between the human host and the sand fleas are taken into consideration, including factors like infestation rate, incubation duration, and recovery rate. We calculate the basic reproduction parameter for the system, symbolized by R0 with the help of the next-generation matrix technique. A novel numerical scheme for encapsulating the non-local and memory-dependent aspects of the system is conceptualized via the Atangana-Baleanu fractional derivative. We prove the existence and uniqueness of the solution of the model of the infection and establish stability of the steady-states of the model. In addition to this, numerical simulations are carried out to evaluate the efficiency of interventions like campaigns for better sanitation and treatment, and to investigate the influence of various management techniques on the prevalence of tungiasis. The outcomes of the numerical simulations give us information about the possible efficacy of different control strategies in lowering the incidence of tungiasis. This research gives quantitative tools to enhance decision-making processes in public health treatments and advances our understanding of the dynamics of the tungiasis. [ABSTRACT FROM AUTHOR]

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam–Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables. [ABSTRACT FROM AUTHOR]

Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious diseases are more prevalent, and healthcare systems may be less equipped to handle them. It is recognized that the hepatitis B virus (HBV) infection remains a critical global public health issue. In this study, we develop a comprehensive model for HBV infection that includes vaccination and hospitalization through a fractional framework. It has been shown that the solutions of the recommended system of HBV infection are positive and bounded. We examine the steady states of the model and determine the basic reproduction number; denoted by R 0 . The qualitative and quantitative behavior of the model is demonstrated using mathematical skills and numerical techniques. It has been proved that the infection-free steady state of the system is locally asymptotically stable if R 0 < 1 and unstable otherwise. Furthermore, the Ulam–Hyers stability (UHS) of the recommended fractional models is investigated and the significant conditions are provided. We present an iterative technique to visualize the dynamical behavior of the system. We perform different simulations to illustrate the effect of different input factors on the solution pathways of the system of HBV infection to conceptualize the role of parameters in the control and prevention of the infection. [ABSTRACT FROM AUTHOR]

It is renowned that the immune reaction in the tumour micro environment is a complex cellular process that requires additional research. Therefore, it is important to interrogate the tracking path behaviour of tumor-immune dynamics to alert policy makers about critical factors of the system. Here, we use fractional derivative to structure tumor-immune interactions. Furthermore, in our research, we concentrated on the qualitative investigation and time series analysis of tumor-immune cell interactions. The solution routes are examined using a new numerical technique to emphasis the impact of the factors on tumor-immune system. We focused on the behaviour of the system with fluctuation of different values. The most crucial components of the proposed system are identified and policymakers are advised. The outcomes of the present study are the strong predictor of clinical success and the in-out of immune cells in a tumour is also critical to treatment efficacy. As a result, studying the behaviour of tumor-immune cell interactions is important to predict crucial factors for the prevention and management to the health officials. [ABSTRACT FROM AUTHOR]

We focused on the analytical analysis of steady flow of nanofluid, viscous dissipation with convective boundary condition in this work. The MWCNT and SWCNT are used to described the nanofluid. A similarity transformation is applied to convert nonlinear PDE from their dimensional form to dimensionless nonlinear ODE. The developed nonlinear ODE for velocity and temperature profiles are solved by using an approximate analytical technique called the homotopy asymptotic method. Graphs are used to discuss and illustrate the results. Graphs are used to interpret the effects of several factors. Finally, the skin friction and Nusselt number are illustrated in the form of table. [ABSTRACT FROM AUTHOR]

The impact of coupled stress casson nanofluid-flow over a stretching surface will be examined in this paper. The fundamental controlling PDE are transformed using the stated similarity transformation into a pair of coupled, non-linear ODE, one for velocity and the other for temperature distribution. The modeled flow problem's approximate analytical solution was discovered using the approximate analytical approach. Graphs are used to illustrate the effects of different factors. A table illustrating the relationship between the Nusselt number and skin friction is provided. [ABSTRACT FROM AUTHOR]

Dengue fever has a huge impact on people's physical, social, and economic lives in low-income locations worldwide. Researchers use epidemic models to better understand the transmission patterns of dengue fever in order to recommend effective preventative measures and give data for vaccine and treatment development. We use fractional calculus to organise the transmission phenomena of dengue fever, including immunisation, reinfection, therapy, and asymptotic carriers. In addition, we focused our study on the dynamical behavior and qualitative approach of dengue infection. The existence and uniqueness of the solution of the suggested dengue dynamics are inspected through the fixed point theorems of Schaefer and Banach. The Ulam-Hyers stability of the suggested dengue model is established. To illustrate the contribution of the input factors on the system of dengue infection, the solution paths are studied using the Laplace Adomian decomposition approach. Furthermore, numerical simulations are used to show the effects of fractional-order, immunity loss, vaccination, asymptotic fraction, biting rate, and therapy. We have established that asymptomatic carriers, bite rates, and immunity loss rates are all important factors that might make controlling more challenging. The intensity of dengue fever may be controlled by reducing mosquito bite rates, whereas the asymptotic fraction is risky and can transmit the illness to noninfected regions. Vaccination, fractional order, index of memory, and medication can be employed as proper control parameters. [ABSTRACT FROM AUTHOR]

The infection of human immunodeficiency virus (HIV) is a serious and potentially incurable infection. There is no cure for HIV and is a public health issue around the world. That is why, it is valuable to investigate the intricate phenomena of HIV infection and provide some control interventions to lessen its economic burden. In this research work, the dynamics of HIV via fractional calculus to conceptualize the intricate phenomena of this viral infection has been formulated and conceptualized. We have shown the rudimentary concept of fractional calculus in Atangana–Baleanu framework. A novel numerical technique is presented for the chaotic and dynamic behaviour of the proposed model. The oscillatory and chaotic phenomena of the system have been shown with the fluctuation of different input factors of the system. Furthermore, we have shown the affect of fractional order on the proposed system of HIV infection. Most critical input parameters are highlighted through numerical simulations and suggested control intervention to the policy makers. Finally, we have shown the stability result and the convergence condition for the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution. [ABSTRACT FROM AUTHOR]

The utilization of time-fractional PDEs in diverse fields within science and technology has attracted significant interest from researchers. This paper presents a relatively new numerical approach aimed at solving two-term time-fractional PDE models in two and three dimensions. We combined the Liouville–Caputo fractional derivative scheme with the Strang splitting algorithm for the temporal component and employed a meshless technique for spatial derivatives utilizing Lucas and Fibonacci polynomials. The rising demand for meshless methods stems from their inherent mesh-free nature and suitability for higher dimensions. Moreover, this approach demonstrates the effective approximation of solutions across both regular and irregular domains. Error norms were used to assess the accuracy of the methodology across both regular and irregular domains. A comparative analysis was conducted between the exact solution and alternative numerical methods found in the contemporary literature. The findings demonstrate that our proposed approach exhibited better performance while demanding fewer computational resources. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of at least two weak solutions to a class of singular two-phase problems with variable exponents involving a ψ-Hilfer fractional operator and Dirichlet-type boundary conditions when the term source is dependent on one parameter. Here, we use the fiber method and the Nehari manifold to prove our results. [ABSTRACT FROM AUTHOR]

The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or uniform nodes, resulting in a sparse and well-conditioned coefficient matrix. The study highlights the advantages of meshless method, particularly their simplicity of implementation in higher dimensions. To validate the accuracy and efficacy of the proposed method, we performed numerical simulations and compared them with analytical solutions for various test problems. These simulations were carried out on computational domains of both rectangular and non-rectangular shapes. The research highlights the potential of meshless techniques in solving complex diffusion problems and its successful applications in groundwater contamination and other relevant fields. [ABSTRACT FROM AUTHOR]

The Lord Shulman swelling porous thermo-elastic soil system with the effects of microtemperature, temperatures and distributed delay terms is considered in this study. The well-posedness result is established by the Lumer–Phillips corollary applied to the Hille–Yosida theorem. The exponential stability result is proven by the energy method under suitable assumptions. [ABSTRACT FROM AUTHOR]

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space. [ABSTRACT FROM AUTHOR]

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 . [ABSTRACT FROM AUTHOR]

In this work, by the use of a semigroup theory approach, we provide a global solution for an initial boundary value problem of the wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. In addition to this, we establish a blow-up result for the solution under the condition of non-positive initial energy. [ABSTRACT FROM AUTHOR]

The economic burden of HIV extends beyond the individual level and affects communities and countries. HIV can lead to decreased economic growth due to lost productivity and increased healthcare costs. In some countries, the HIV epidemic has led to a reduction in life expectancy, which can impact the overall quality of life and economic prosperity. Therefore, it is significant to investigate the intricate dynamics of this viral infection to know how the virus interacts with the immune system. In the current research, we will formulate the dynamics of HIV infection in the host body to conceptualize the interaction of T-cells and the immune system. The recommended model of HIV infection is presented with the help of fractional calculus for more precious outcomes. We introduce numerical methods to demonstrate how the input parameters affect the output of the system. The dynamical behavior and chaotic nature of the system are visualized with the variation of different input factors. The system's tracking path has been numerically depicted and the impact of the viruses on T-cells has been demonstrated. In addition to this, the key factors of the system has been predicted through numerical findings. Our results predict that the strong non-linearity of the system is responsible for the chaos and oscillation, which are so closely related. The chaotic parameters of the system are highlighted and are recommended for the control of the chaos of the system. [ABSTRACT FROM AUTHOR]

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions Δ a LC μ f (a + J 0 + 1 − μ) ≥ (1 − μ) f (a + J 0) and Δ a LC μ f (a + J 0 + 1 − μ) ≤ (1 − μ) f (a + J 0) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results. [ABSTRACT FROM AUTHOR]

Theoretical influence of the buoyancy and thermal radiation effects on the MHD (magnetohydrodynamics) flow across a stretchable porous sheet were analyzed in the present study. The Darcy–Forchheimer model and laminar flow were considered for the flow problem that was investigated. The flow was taken to incorporate a temperature-dependent heat source or sink. The study also incorporated the influences of Brownian motion and thermophoresis. The general form of the buoyancy term in the momentum equation for a free convection boundary layer is derived in this study. A favorable comparison with earlier published studies was achieved. Graphs were used to investigate and explain how different physical parameters affect the velocity, the temperature, and the concentration field. Additionally, tables are included in order to discuss the outcomes of the Sherwood number, the Nusselt number, and skin friction. The fundamental governing partial differential equations (PDEs), which are used in the modeling and analysis of the MHD flow problem, were transformed into a collection of ordinary differential equations (ODEs) by utilizing the similarity transformation. A semi-analytical approach homotopy analysis method (HAM) was applied for approximating the solutions of the modeled equations. The model finds several important applications, such as steel rolling, nuclear explosions, cooling of transmission lines, heating of the room by the use of a radiator, cooling the reactor core in nuclear power plants, design of fins, solar power technology, combustion chambers, astrophysical flow, electric transformers, and rectifiers. Among the various outcomes of the study, it was discovered that skin friction surges for 0.3 ≤ F 1 ≤ 0.6, 0.1 ≤ k 1 ≤ 0.4 and 0.3 ≤ M ≤ 1.0, snf declines for 1.0 ≤ G r ≤ 4.0. Moreover, the Nusselt number augments for 0.5 ≤ R ≤ 1.5, 0.2 ≤ N t ≤ 0.8 and 0.3 ≤ N b ≤ 0.9, and declines for 2.5 ≤ P r ≤ 5.5. The Sherwood number increases for 0.2 ≤ N t ≤ 0.8 and 0.3 ≤ S c ≤ 0.9, and decreases for 0.1 ≤ N b ≤ 0.7. [ABSTRACT FROM AUTHOR]

The subject of this research is a coupled system of nonlinear viscoelastic wave equations with distributed delay components, infinite memory and Balakrishnan-Taylor damping. Assume the kernels holds true the below in which and are functions. We demonstrate the stability of the system under this highly generic assumptions on the behaviour of at infinity and by dropping the boundedness assumptions in the historical data. [ABSTRACT FROM AUTHOR]

In this research, we investigate the presence of weak positive solutions for a family of anisotropic non-local elliptic systems in bounded domains using the sub-super solutions approach in conjunction with Schauder's fixed point. [ABSTRACT FROM AUTHOR]

Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann–Liouville type by considering the positivity of ∇ b 0 R L θ g (z) combined with a condition on g (b 0 + 2) , g (b 0 + 3) and g (b 0 + 4) , successively. The article ends with a relationship between the discrete nabla fractional and integer differences of the Riemann–Liouville type, which serves to show the monotonicity of the discrete fractional difference ∇ b 0 R L θ g (z) . [ABSTRACT FROM AUTHOR]

In this study, we implemented the well-known Crank–Nicolson scheme for the numerical solution of Schrödinger equation. The numerical results converge to the exact solution because the Crank–Nicolson scheme is unconditionally stable and accurate. We have compared the results for different parameters with analytical solution, and it is found that the Crank–Nicolson scheme is suitable for the numerical solution of Schrödinger equations. Three different problems are included to verify the accuracy, stability, and capability of the Crank–Nicolson scheme. [ABSTRACT FROM AUTHOR]

In this study, we implemented the well-known Crank–Nicolson scheme for the numerical solution of Schrödinger equation. The numerical results converge to the exact solution because the Crank–Nicolson scheme is unconditionally stable and accurate. We have compared the results for different parameters with analytical solution, and it is found that the Crank–Nicolson scheme is suitable for the numerical solution of Schrödinger equations. Three different problems are included to verify the accuracy, stability, and capability of the Crank–Nicolson scheme. [ABSTRACT FROM AUTHOR]

The heat transfer ratio has an important role in industry and the engineering sector; the heat transfer ratios of CNT nanofluids are high compared to other nanofluids. This paper examines the analytical investigation of the time-dependent stagnation point flow of a CNT nanofluid over a stretching surface. For the investigation of the various physical restrictions, single and multi-walled carbon nanotubes (SWCNTs, MWCNTs) were used and compared. The defined similarity transformation was used, to reduce the given nonlinear partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). The model nonlinear ordinary differential equations were solved, with an approximate analytical (OHAM) optimal homotopy asymptotic method being used for the model problem. The impact of different parameters such as magnetic field parameter, unsteady parameter, dimensionless nanoparticles volume friction, Prandtl number, and Eckert number are interpreted using graphs, in the form of the velocity and temperature profile. [ABSTRACT FROM AUTHOR]

The abnormal growth of cells in the breast is called malignancy or breast cancer; it is a life-threatening and dangerous cancer in women around the world. In the treatment of cancer, the doctors apply different techniques to stop cancer cell development, remove cancer cells through surgery, or kill cancer cells. In chemotherapy treatment, powerful drugs are used to kill abnormal cells; however, it has adverse reactions on the patient heart which is called cardiotoxicity. In this paper, we formulate the dynamics of cancer in the breast with adverse reactions of chemotherapy treatment on the heart of a patient in the fractional framework to visualize its dynamical behaviour. We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. Furthermore, the Adams-Bashforth numerical technique is presented for the solution of fractional-order system to illustrate the time series of breast cancer model. The dynamical behaviour of different stages of breast cancer is then highlighted numerically to show the effect of fractional-order ϑ and to visualize the role of input parameter on the dynamics of breast cancer. [ABSTRACT FROM AUTHOR]

The behavior of hybrid nanofluid and stagnation point flow toward a stretched surface along with melting heat transfer, second-order slip, electric field, and magnetic field effect is investigated in this study. Hybrid nanoparticles alumina A l 2 O 3 and copper (Cu) are considered with the base fluids water H 2 O . The PDEs with corresponding boundary constraints are transformed into a set of nonlinear ODEs using similarities transformation. The set of nonlinear ODEs are analyzed analytically using semianalytical method HAM in Mathematica software. Dual solution is determined which relaying on the emerging parameters included magnetic field, volume fractions, electric field, dimensionless surface velocity slip factors, Eckert number, and Prandtl number. The results are shown in the velocity and temperature curves as well as skin friction coefficient and local Nusselt number. The analysis shows that velocity profile is an increasing function of slip parameter, electric field, while reducing function of magnetic field. Temperature profile is an increasing function of magnetic field parameter, electric field parameter, volume fraction parameter, and Eckert number, while reducing function of Prandtl number. The main outcomes are as follows that hybrid nanofluids are higher thermal properties as compared to conventional fluids. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, and soaps as well. [ABSTRACT FROM AUTHOR]

In this paper, the Darcy–Forchheimer laminar thin film flow with MHD and heat transfer on an unsteady horizontal stretched surface is investigated. The impact of thermal radiation and viscous dissipation is also considered for thin film flow. The analysis of heat source with thermal radiation in a boundary layer flow can play a great role in manufacturing engineering procedures such as the production of electric power, solar energy modernization, and astrophysical flow. By using similarity transformation, the system of PDEs is converted to ODEs. Then HAM is applied for the solution of the problem. Moreover, the velocity and temperature profile for various embedded variables are discussed through graphs while the numerical solution of concerned physical quantities such as skin friction and Nusselt number are discussed through tables. The analysis shows that velocity profile is reducing function of M , K 1 , S , and F 1 . The temperature profile is an increasing function S and E c while a reducing function of Pr and R. The overall behavior of the proposed system is highlighted analytically. [ABSTRACT FROM AUTHOR]

This article develops the semianalytical analysis of couple stress hybrid nanofluid free stream past a rotating disc by applying the magnetic flux effects and radiation of thermal energy. The analysis of such kind of mixed convective flow is most important due to numerous industrial applications such as electronic devices, atomic reactors, central solar energy equipment, and heat transferring devices. The impact of variable permeability is also considered in the study. The permeability of the disc obeys the Darcy-Forchheimer model. The hybrid nanofluid is composed of water, titanium dioxide, and aluminum oxide. The set of governing equations in the PDE form are transformed to couple ODEs by applying similarity transformations. The ODE set are solved by applying the technique of HAM. The graphs of impacts of numerous physical parameters over momentum, energy, and concentration profiles are drawn in computer-based application Mathematica 11.0.1. In the sundry physical parameters, the porosity parameter, Reynolds number, inertial parameter, Prandtl number, Schmidt number, couple stress, and quotient of rotational momentum to elongating rate are included. During the analysis, it is found that the momentum profile of the couple stress hybrid nanofluid enhances with local inertial parameter, couple stress parameter, porosity parameter, and Reynolds number but declines for the growth in Hartmann number. Heat transfer rate enhances for radiation parameter but decreases in variable for temperature, thermal stratification parameter, thermophoresis parameter, and Brownian parameter. [ABSTRACT FROM AUTHOR]

This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs. [ABSTRACT FROM AUTHOR]

In this paper, the steady electrically conducting hybrid nanofluid (CuO-Cu/blood) laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms is considered. Additionally, hybrid nanofluid flow over a horizontal porous stretching sheet along with an induced magnetic field and external magnetic field effects that can be used in biomedical fields, such as in drug delivery and the flow dynamics of the microcirculatory system. This investigation can also deliver a perfect view about the mass and heat transfer behavior of blood flow in a circulatory system and various hyperthermia treatments such as the treatment of cancer. The simple partial differential equations (PDEs) are converted into a series of dimensional ordinary differential equations (ODEs), which are determined using appropriate similarities variables (HAM). The influence of the suction or injection parameter, mixed convection, Prandtl number, buoyancy ratio parameter, permeability parameter, magnetic parameter, reciprocal magnetic prandtl number, bioconvection Rayleigh number, coupled stress parameter, thermophoretic parameter, Schmidt number, inertial parameter, heat source parameter, and Brownian motion parameter on the concentration, motile microorganisms, velocity, and temperature is outlined, and we study the physical importance of the present problem graphically. [ABSTRACT FROM AUTHOR]