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In contemporary times, there has been a significant focus among researchers on hybrid nanofluids derived from oils, owing to their remarkable and substantial utility in the domains of engineering, mechanics, and industrial applications. The aim of this research is to determine the impact of incorporating tantalum and nickel nanoparticles in mineral oil on thermal characteristics and flow patterns, with the objective of predicting possible improvements. The dependence of the role of both nanoparticles on their shapes is evaluated for column, platelet, lamina, cylinder, and tetrahedron-type shapes. This work analyzes the thermal performance of two different nanofluids individually made of tantalum and nickel nanoparticles while also examining the synergistic effects produced due to the simultaneous suspension of these particles. A profound understanding of the intricate flow dynamics and thermal energy transfer phenomena along a vertical surface holds paramount importance in the pursuit of optimizing heat exchange procedures, formulating effective cooling systems, and designing thermally efficient devices. Furthermore, it contributes to the advancement of climate modeling, the precision of weather forecasting, and the refinement of the operational effectiveness of solar thermal systems. The basic mathematical model is formulated subject to free convection, time-dependent flow and heat conditions, and thermal radiation. This governing system is made non-dimensional to lessen the intricacy and provide the basis for the utilization of fractional operators. In order to assess the effectiveness of fractional modeling techniques, constant proportional Caputo (CPC) and Atangana–Baleanu (ABC) derivatives are operated for the model generalization. Most of the time, solving fractional models via an analytic method are not a feasible technique because it produces extremely complex and implicit mathematical expressions. However, in this study, the Laplace transform is served as a solution procuring technique, and series and integral form exact solutions are extracted for CPC and ABC derivative-based models, respectively. To interpret modifications in thermal and velocity patterns arising from diverse physical phenomena, numerous graphical depictions of exact solutions are communicated. Moreover, the implications of varying a number of critical factors, including the fractional parameter, nanoparticles' shapes and proportions, and radiation term, on shear stress and thermal productivity of the hybrid nanofluid are discussed using the tabulated findings. On comparing shape effects and individual suspensions of considered nanoparticles, it is observed that lamina shape and nickel nanoparticles are relatively more effective regarding the improvement of thermal performance. The model based on the CPC derivative yields lower profiles of temperature and flow functions as compared to the ABC derivative-based model. The results indicate that introducing homogeneous proportions of tantalum and nickel nanoparticles into mineral oil raises its heat-transferring capacity by up to 47.60%. These findings suggest that the examined hybrid nanofluid performs extremely well as a lubricant and a cooling agent. [ABSTRACT FROM AUTHOR]

Enriched multi-valued contraction mappings and enriched multi-valued nonexpansive mappings are introduced in the context of geodesic spaces, and their fixed points are analyzed in CAT(0) spaces. For the contraction mapping, the existence of a fixed point is established, and a scheme for approximating the point is provided. Conditions under which a sequence converges to a fixed point of the enriched multi-valued nonexpansive mapping are given, and the mapping is shown to exhibit a demiclosedness-type property. Furthermore, it is shown that the fixed point set of the mapping is closed and convex. Conditions under which a sequence converges to a Mann-type scheme are given, and an application to an equilibrium problem involving Nash non-cooperative games is discussed. [ABSTRACT FROM AUTHOR]

Solving systems of nonlinear equations has evolved into an active research field, with numerous iterative methods being proposed. Notably, iterative methods characterized by fast convergence remain of interest. In this paper, based on the modified line search scheme by Ou and Li, we introduce a derivative-free algorithm with a relaxed-inertial technique for approximating solutions of nonlinear systems involving pseudo-monotone mappings in Euclidean space. The global convergence of the proposed algorithm is established without Lipschitz continuity of the underlying mapping. Moreover, our approach allows flexibility in selecting the inertial extrapolation step length within the interval [0, 1]. To show the efficiency of the proposed method, we embed a derivative-free search direction into the scheme. Numerical experiments are given to illustrate the efficiency of the proposed algorithm for large-scale systems and sparse signal reconstruction. [ABSTRACT FROM AUTHOR]

This article communicates Cattaneo-Christov heat and mass flux theory in the flow of Maxwell nanofluid and gyrotactic microorganisms towards a spinning disk with the effects of Hall current, and Darcy porous medium. Entropy generation is also taken into account in the presence of Brownian motion, thermophoresis, thermal radiation, heat source/sink, and chemical reaction. Non-dimensional equations are derived for the velocities, temperature, nanoparticles concentration, and motile gyrotactic microorganisms concentration with the help of similarity transformations. Homotopy analysis method (HAM) is used to obtain the solution. Graphs and a table are plotted to show the effects of physical parameters. Numerical computations are given to analyze the values of skin friction coefficients which present a nice agreement with the published results. [ABSTRACT FROM AUTHOR]

This paper provides an iterative construction for a common solution associated with the pseudomonotone equilibrium problems, fixed point problem of a finite family η -demimetric operators and the generalized split null point problem in Hilbert spaces. The sequence of approximants is a variant of the parallel shrinking extragradient algorithm with the inertial effect converging strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we study two methods exhibiting strong convergence for solving classical variational inequality problems with Lipschitz-continuous and pseudomonotone operators in a real Hilbert space. These methods are inspired by Tseng's extragradient method, as well as the viscosity and Mann-type methods, both incorporating a straightforward step-size rule. These methods use variable step sizes that are modified at each iteration and dependent on prior iterations. These methods also have the additional advantage of not requiring prior knowledge of the Lipschitz constant or a linesearch process. The convergence for both methods is established under mild conditions. A series of numerical experiments is performed to validate the efficacy and superiority of the presented iterative methods over existing state-of-the-art methods. These experiments serve to affirm the effectiveness of the proposed methods in solving variational inequality problems in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this work, we propose an iterative method for finding a common solution of a variational inclusion problem involving a maximally monotone operator and a fixed point problem for a pseudocontractive mapping in real Hilbert space. Under some standard and easy-to-verify conditions, we establish that the sequence generated by the proposed method converges strongly to a solution of the considered problem. Numerical illustrations and application in image recovery suggest that the proposed method is easy to implement and efficient. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inertial accelerated outer quadratic approximation method for solving the split feasibility problem in Hilbert spaces. The algorithm uses projections onto closed balls approximations of the original split feasibility problem involved sets. Since the projection onto the closed ball has a closed form, the proposed method is thus convenient to implement. Moreover, it uses a self-adaptive step-size which does not need any prior information of the operator norm. Under some suitable assumptions, we establish and prove a strong convergence theorem for the proposed algorithm. Finally, we provide several numerical experiments to demonstrate the performances of our proposed method. We also give the applications of our result to elastic nets. Our method generalizes and improves many results in the literature. [ABSTRACT FROM AUTHOR]

In recent years, many subclasses of univalent functions, directly or not directly related to the exponential functions, have been introduced and studied. In this paper, we consider the class of S e ∗ for which z f ′ (z) / f (z) is subordinate to e z in the open unit disk. The classic concept of Hankel determinant is generalized by replacing the inverse logarithmic coefficient of functions belonging to certain subclasses of univalent functions. In particular, we obtain the best possible bounds for the second Hankel determinant of logarithmic coefficients of inverse starlike functions subordinated to exponential functions. This work may inspire to pay more attention to the coefficient properties with respect to the inverse functions of various classes of univalent functions. [ABSTRACT FROM AUTHOR]

This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results. [ABSTRACT FROM AUTHOR]

This article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of the circular intuitionistic fuzzy set model that improves its performance thanks to the acclaimed extension of intuitionistic fuzzy sets to Pythagorean fuzzy sets. Then, we generalize C-PFSs to produce the novel disc Pythagorean fuzzy sets (D-PFSs). The constituent elements of both C-PFSs and D-PFSs are circular Pythagorean fuzzy values, either with a common or a distinctive radius. We lay out some fundamental algebraic and arithmetic operations on D-PFSs (hence on C-PFSs), namely union, intersection, addition, multiplication, and scalar multiplication, and we explore the main features of these operations. We propose and investigate the properties of the novel circular Pythagorean fuzzy weighted average/geometric aggregation operators. The "COmbinative Distance based ASsesment" approach, which is based on the Hamming and Euclidean distances, is expanded to the D-PFS framework. To justify its implementability, we apply the new methodology to a case study (selection of the best supermarkets to buy fresh fruit for a hotel) and then we compare it to related solutions. [ABSTRACT FROM AUTHOR]

Engine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape CuO , platelet shape Al 2 O 3 and cylindrical shape TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil. [ABSTRACT FROM AUTHOR]

The current article aims to examine the magnetohydrodynamics (MHD) impact on the flow of MgO–Ag/water-based hybrid nanoliquid with motile microorganisms and the fluid is allowed to flow over a Riga plate subject to slip effects and activation energy. Furthermore, the presence of a uniform heat source/sink is also addressed in the energy equation. In addition to this, the thermophoresis effect is highlighted in the concentration equation. From the present proposed model, we get a non-linear system of the governing equations. The obtained system of partial differential equations (PDEs) is converted to the dimensionless system of ordinary differential equations (ODEs) using the similarity transformation. The obtained high non-linear system of equations has been solved numerically, using the parametric continuation method (PCM). In the present analysis, the main motivation is to highlight the heat transfer rate of MgO–Ag/water-based hybrid nanofluid flow over a Riga plate. The second motivation of the present research is to highlight the impact of slip conditions on the velocity, energy, and mass profiles. From the graphical analysis, it is depicted that the slip conditions reduce the velocity, energy, and mass outlines. From the present analysis, we concluded that volume friction reduced the flow profile while increasing the temperature of the fluid flow over a Riga plate. All the parameters of the present research are highlighted in velocity temperature and concertation of the fluid. In addition to this in all the figures we have compared the hybrid nanofluid with mono nanofluid and the also the comparison between slip and no-slip conditions have carried out through graphs for velocity, temperature, and concentration. [ABSTRACT FROM AUTHOR]

This research article develops two adaptive, efficient, structured non-linear least-squares algorithms, NLS. The approach taken to formulate these algorithms is motivated by the classical Barzilai and Borwein (BB) (IMA J Numer Anal 8(1):141–148, 1988) parameters. The structured vector approximation, which is an action of a vector on a matrix, is derived from higher order Taylor series approximations of the Hessian of the objective function, such that a quasi-Newton condition is satisfied. This structured approximation is incorporated into the BB parameters' weighted adaptive combination. We show that the algorithm is globally convergent under some standard assumptions. Moreover, the algorithms' robustness and effectiveness were tested numerically by solving some benchmark test problems. Finally, we apply one of the algorithms to solve a robotic motion control model with three degrees of freedom, 3DOF. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space ℓ 2 , with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader's strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples. [ABSTRACT FROM AUTHOR]

In this work, a phase- and amplification-fitted 5(4) diagonally implicit pair of Runge–Kutta–Nyström methods with four stages is developed to solve special second-order ordinary differential equations (ODEs), whose solutions are oscillatory. The local truncation errors of the formulas of the new pair are given, showing that the orders are maintained, with respect to the original formulas. The stability of the new method is studied, showing that the developed formulas present non-vanishing intervals of absolute stability. The numerical examples considered clearly show the robustness of the developed embedded pair over other diagonally implicit Runge–Kutta–Nyström (DIRKN) pairs in the literature. [ABSTRACT FROM AUTHOR]

During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called "ternary hybrid nanofluid". In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide Fe 3 O 4 , platelet shaped zinc Zn , and cylindrical shaped gold Au , which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction ϕ hnf of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction ϕ hnf of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped Fe 3 O 4 enhances up-to 4.63%, platelet shaped Zn nanoparticles enhances up-to 8.984% and cylindrical shaped gold Au nanoparticles enhances up-to 10.407%. [ABSTRACT FROM AUTHOR]

The core devotion of this study is to develop a generalized model by means of a recently proposed fractional technique in order to anticipate the enhancement in the thermal efficiency of engine oil because of the dispersion of graphene and magnesia nanoparticles. In addition to investigating the synergistic attributes of the foregoing particles, this work evaluates shape impacts for column, brick, tetrahedron, blade, and lamina-like shapes. In the primary model, the flow equation is coupled with concentration and energy functions. This classical system is transmuted into a fractional environment by generalizing mathematical expressions of thermal and diffusion fluxes by virtue of the Prabhakar fractional operator. In this study, ramped flow and temperature slip conditions are simultaneously applied for the first time to examine the behavior of a hybrid nanofluid. The mathematical analysis of this problem involves the incorporation of dimension-independent parameters into the model and the execution of the Laplace transform for the consequent equations. By doing so, exact solutions are derived in the form of Mittag–Leffler functions. Multiple illustrations are developed by dint of exact solutions to chew over all aspects of temperature variations and flow dynamics. For the preparation of these illustrations, the details of parametric ranges are as follows: 0.00 ≤ Υ ≤ 0.04 , 2.0 ≤ G r 1 ≤ 8.0 , 0.5 ≤ S c ≤ 2.0 , 0.1 ≤ τ ≤ 4.0 , 0.1 ≤ d ≤ 0.6 , 0.2 ≤ λ 1 ≤ 1.5 , and 1.0 ≤ G r 2 ≤ 7.0 . The contribution of differently shaped nanoparticles, volume proportions, and fractional parameters in boosting the heat-transferring attributes of engine oil is also anticipated. In this regard, results for Nusselt number are provided in tabular form. Additionally, a brief analysis of shear stress is carried out for fractional parameters and various combinations of magnesia, graphene, and engine oil. This investigation anticipates that engine oil's hybridization with magnesia and graphene would result in a 33% increase in its thermal performance, which evidently improves its industrial significance. The enhancement in Schmidt number yields an improvement in the mass transfer rate. An increment in collective volume fraction leads to raising the profile of the thermal field. However, the velocity indicates a decreasing behavior. Nusselt number reaches its highest value ( N u = 8.1363 ) for the lamina shape of considered particles. When the intensity of the buoyancy force augments, it causes the velocity to increase. [ABSTRACT FROM AUTHOR]

Due to the important application of magnetohydrodynamic in cancer tumor treatment, magnetic drug targeting, magnetic endoscopy, magnetic devices for cell separation, fluid pumping in industrial and engineering developments, and adjusting blood flow during surgery. Therefore, we investigate the relative magnetic field analysis of the two-phase fluctuating flow of Casson dusty fluid over a parallel plate. More exactly, the relative magnetic phenomena are fixed relative to the fluid (MFFRF) or fixed relative to the plate (MFFRP). Moreover, the entropy generation and Bejan numbers analysis are also considered for both MFFRF and MFFRP. The mathematical modeling was established as the set of partial differential equations for dusty Casson fluid. Buckingham's pi theorem is used to find out the dimensionless variables, to make our system dimensionless. The perturb solution is to find out by incorporating Poincare–Lighthill perturbation technique. To know in-depth different parameters, the graphical results for both velocities are plotted with the help of Mathcad-15 software. It is observed that the relative magnetic field plays an important role in the fluid as well as particle motion. The relative magnetic field is affecting the entropy generation as well as the Bejan number. This study will help out in the adjusting of blood flow during surgery and fluid pumping in industrial and engineering process. [ABSTRACT FROM AUTHOR]

In this paper, a Halpern–Tseng-type algorithm for approximating zeros of the sum of two monotone operators whose zeros are J-fixed points of relatively J-nonexpansive mappings is introduced and studied. A strong convergence theorem is established in Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorem to convex minimization and image-restoration problems are presented. In addition, the proposed algorithm is used in solving some classical image-recovery problems and a numerical example in a Banach space is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

A family of inertial extragradient-type algorithms is proposed for solving convex pseudomonotone variational inequality with fixed-point problems, where the involved mapping for the fixed point is a ρ-demicontractive mapping. Under standard hypotheses, the generated iterative sequence achieves strong convergence to the common solution of the variational inequality and fixed-point problem. Some special cases and sufficient conditions that guarantee the validity of the hypotheses of the convergence statements are also discussed. Numerical applications in detail illustrate the theoretical results and comparison with existing methods. [ABSTRACT FROM AUTHOR]

An incredible eradication of thermal indulgence is required to enhance the flow and heat transfer enhancement in micro/nanofluidic devices. In addition, the rapid transport and instantaneous mixing of colloidal suspensions of metallic particles at nanoscale are exceptionally crucial at ascendency of inertial and surface forces. To address these challenges, the present work is intended to investigate the role of trimetallic nanofluid comprising of three kinds of nano-sized granules (titanium oxide, Silica and Aluminium dioxide) with pure blood through a heated micropump in the presence of inclined magnetic field and axially implemented electric field. To ensure rapid mixing in unidirectional flow, the pump internal surface is lined-up with mimetic motile cilia with slip boundary. The embedded cilia whip in pattern due to dynein molecular motion controlled by time and produce a set of metachronal waves along the pump wall. The shooting technique is executed to compute the numerical solution. In a comparative glance it is revealed that the trimetallic nanofluid exhibits 10% higher heat transfer efficiency as compared to bi-hybrid and mono nanofluids. Moreover, the involvement of electroosmosis results in almost 17% decrease in the heat transfer rate if it values jumps from 1 to 5. The fluid temperature in case of trimetallic nanofluid is higher and thus keeps the heat transfer entropy and the total entropy lower. Furthermore, involvement of thermal radiated and momentum slip significantly contribute in reducing heat losses. [ABSTRACT FROM AUTHOR]

The present problem is offered for the visualization of the MHD flow of non-Newtonian Cross-hybrid nanoliquid with the application of Darcy–Forchheimer through the porous medium toward the moving thin needle. Further, the present work described the engineering applications of the non-Newtonian fluids. Commonly, the non-Newtonian liquids are useful for lubricating purposes including greases and Engine oil (EO), etc. Additionally, the computations for Hall current and viscous dissipation are deliberated for the enhancement of flow behavior. The heat transmission phenomenon is discussed under the Cattaneo–Christov heat flux theory instead of Fourier's law. Engineering applications of the homogeneous and heterogeneous chemical reactions are analyzed in the current analysis. EO has an enormous application in the engineering fields, and therefore in the present work EO is used as a base liquid and molybdenum disulfide MoS 2 and graphene oxide GO are the nanoparticles. The hybrid nanofluid showed more satisfactory results in the enhancement of the heat transport in the engineering fields as compared to the nanofluids and regular fluids; therefore the MoS 2 and GO are mix-ups in the EO. The present model is developed in the form of PDEs which can be altered into ODEs through the execution of suitable similarity transformations. A homotopic analysis scheme is adopted for the analytic simulation of the transformed ODEs. The velocity, energy, and mass curves are computed against different flow parameters in a pictorial form. Skin friction and Nusselt in contour graphs are discussed. Key findings from this inspection are that both nanoparticle volume fractions declined the velocity profile but augmented the temperature of the hybrid nanoliquid. Further, it is noted that boosting the Schmidt has significantly reduced the hybrid nanofluid concentration. [ABSTRACT FROM AUTHOR]

In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature. [ABSTRACT FROM AUTHOR]

Many efforts have been made to develop efficient algorithms for solving system of nonlinear equations due to their applications in different branches of science. Some of the classical techniques such as Newton and quasi-Newton methods involve computing Jacobian matrix or an approximation to it at every iteration, which affects their adequacy to handle large scale problems. Recently, derivative-free algorithms have been developed to solve this system. To establish global convergence, most of these algorithms assumed the operator under consideration to be monotone. In this work, instead of been monotone, our operator under consideration is considered to be pseudomonotone which is more general than the usual monotonicity assumption in most of the existing literature. The proposed method is derivative-free, and also, an inertial step is incorporated to accelerate its speed of convergence. The global convergence of the proposed algorithm is proved under the assumptions that the underlying mapping is Lipschitz continuous and pseudomonotone. Numerical experiments on some test problems are presented to depict the advantages of the proposed algorithm in comparison with some existing ones. Finally, an application of the proposed algorithm is shown in motion control involving a 3-degrees of freedom (DOF) planar robot arm manipulator. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized class of nonexpansive mappings in the setting of CAT p (0) spaces and establish that the mappings have a demiclosedness-type property. We state some conditions under which a sequence Δ -converges to a fixed point of any given map having such fixed point. Also, we introduce JK iteration in CAT p (0) setting and prove some convergence theorems. Furthermore, we apply the result to solve minimization problems in CAT(0) spaces, compute mean and medium, and track a task in robotic motion control. Finally, we give numerical examples in a CAT p (0) space that is not CAT(0) space and in a non-Hilbert CAT(0) space, to show the implementation of the proposed scheme. [ABSTRACT FROM AUTHOR]

In the pump of different machines, the vacuum pump oil (VPO) is used as a lubricant. The heat rate transport mechanism is a significant requirement for all industries and engineering. The applications of VPO in discrete fields of industries and engineering fields are uranium enrichment, electron microscopy, radio pharmacy, ophthalmic coating, radiosurgery, production of most types of electric lamps, mass spectrometers, freeze-drying, and, etc. Therefore, in the present study, the nanoparticles are mixed up into the VPO base liquid for the augmentation of energy transportation. Further, the MHD flow of a couple stress nanoliquid with the applications of Hall current toward the rotating disk is discussed. The Darcy-Forchheimer along with porous medium is examined. The prevalence of viscous dissipation, thermal radiation, and Joule heating impacts are also considered. With the aid of Cattaneo-Christov heat-mass flux theory, the mechanism for energy and mass transport is deliberated. The idea of the motile gyrotactic microorganisms is incorporated. The existing problem is expressed as higher-order PDEs, which are then transformed into higher-order ODEs by employing the appropriate similarity transformations. For the analytical simulation of the modeled system of equations, the HAM scheme is utilized. The behavior of the flow profiles of the nanoliquid against various flow parameters has discoursed through the graphs. The outcomes from this analysis determined that the increment in a couple-stress liquid parameter reduced the fluid velocity. It is obtained that, the expansion in thermal and solutal relaxation time parameters decayed the nanofluid temperature and concentration. Further, it is examined that a higher magnetic field amplified the skin friction coefficients of the nanoliquid. Heat transport is increased through the rising of the radiation parameter. [ABSTRACT FROM AUTHOR]

Inclusion of nanoparticles boosts thermal performance and is essential for thermal transport. The current investigation has been made to conduct research on heat mass transport in synovial material with the mixing of hybrid and tri-hybrid comprising variable viscosity past over a heated surface having constant density and a steady environment. The conservation laws have been considered in the presence of Lorentz force, heat generation/absorption, modified heat and mass fluxes together with chemical reaction. The mathematical model is developed in Cartesian coordinate in the form of coupled partial differential equation (PDEs). The derived PDEs are simplified by a boundary layer approach (BLA) and reduced PDEs have been converted into ordinary differential equation (ODEs) using scaling group Similarity transformation. The converted ODEs are highly nonlinear and have been solved numerically by finite elements scheme (FES). The used scheme is effective for nonlinear problem and can be frequently utilized to tackle nonlinear problems arising in mathematical physics. [ABSTRACT FROM AUTHOR]

The research of fluid containing nanoparticles for the heat transport characteristics is very famous because of its variety of real-life applications in various thermal systems. Although the thermal efficiency of the nanofluid was effective but still the nano scientists were trying to introduce some new advance class of fluid. Therefore, an advance class of fluid is developed by the dispersion of two different nano sized particles in the conventional base fluid known as "Hybrid nanofluid" which is more effective compared to simple nanofluids in many engineering and industrial applications. Therefore, motivated from the hybrid type of nanofluids in the current research we have taken two-dimensional laminar and steady flow of second grade fluid passing through porous plate. The engine oil base fluid is widely used fluid in the engineering and industrial problems. Keeping these applications in mind the engine oil is considered and two different nanoparticles Copper and aluminum oxide are added in ordered to get the required thermal characteristics. In addition to this the thermal radiation, chemical reaction, activation energy, Brownian motion and thermophoresis are also addressed during the current research. The present proposed higher-order PDE's is transformed to the non-linear system of ODE's. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the present analysis and experimental study, it has been proved that the performance of hybrid nanofluid is efficient in many situations compared to nanofluid and regular fluid. For physical interpretation all the flow parameters are discussed through graphs. The impact of volume fraction is also addressed through graphs. Moreover, the comparative analysis between hybrid and nanofluid is carried out and found that hybrid nanofluid performed well as compared to nanofluid and regular fluid. The engineering quantities obtained from the present research have been presented in tables. [ABSTRACT FROM AUTHOR]

This paper concentrated on the multiple generalized report of entropy generation of MHD Casson fluid via Caputo–Fabrizio (CF), Caputo (C), and Atangana–Baleanu (AB) fractional derivative. The ramped wall temperature on the plate while slipping condition on fluid velocity is considered. The mathematical model is made up of a collection of partial differential equations having physical boundaries. Triple fractional definitions are used to generalize the model and solve via joint Laplace and Zakian's numerical algorithm. The fractional results of entropy generation, velocity profile, temperature profile and Bejan number are also evaluated and compared for all three mentioned fractional operators as an objective of the present study. Entropy production can be maximize/ minimize through various physical parameters. The rate of heat transmission may be controlled by increasing the Prandtl number in isothermal temperature and boosting with the ramping wall temperature. It is indicated that Caputo model has maximum velocity and entropy generation in case of isothermal temperature besides Caputo–Fabrizio, and Atangana–Baleanu, while in case of ramped temperature, the phenomena is revised. The combined influence of slipping condition and ramped wall temperature rapidly boosts Casson fluid's velocity and entropy generation. [ABSTRACT FROM AUTHOR]

In this article, we propose a hybrid iterative scheme with strong convergence property for solving variational inequality problems. The algorithm uses a self-adaptive stepsize defined using a simple updating rule. Therefore, the method does not require prior knowledge of the Lipschitz constant of the underlying operator. We consider a more general set of operators as the underlying operators. Moreover, we derived a fixed stepsize scheme from the proposed method. Under some suitable conditions, we show the strong convergence of the iterates generated by the proposed and the derived algorithms. Furthermore, we present numerical experiments to illustrate the computational performance of the proposed algorithm in comparison with some of the existing algorithms in the literature. Additionally, as an application, we use the proposed algorithm to solve the problem of recovering an original signal from a noisy signal [ABSTRACT FROM AUTHOR]

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively. [ABSTRACT FROM AUTHOR]

With the help of CN-inequality, we study fixed point of multi-valued mappings with closed bounded images and establish some strong convergence theorems involving a countable family of demicontractive mappings in Hadamard spaces. Furthermore, we use the established theorems to deduce some theorems involving a family of minimization problems, variational inequality problems, and monotone inclusion problems. We finally give examples to illustrate the results. The results obtained herein generalise some recent results in the literature. [ABSTRACT FROM AUTHOR]

The mechanism of thermal transport can be enhanced by mixing the nanoparticles in the base liquid. This research discusses the utilization of nanoparticles (tri-hybrid) mixture into Carreau–Yasuda material. The flow is assumed to be produced due to the stretching of vertical heated surface. The phenomena of thermal transport are modeled by considering Joule heating and heat generation or absorption involvement. Additionally, activation energy is engaged to enhance heat transfer rate. The mathematical model composing transport of momentum, heat and mass species is developed in Cartesian coordinate system under boundary layer investigation in the form of coupled nonlinear partial differential equations. The complex partial differential equations are converted into coupled nonlinear ordinary differential equations by using the appropriate similarity transformation. The conversion of PDEs into ODEs make the problem easy to handle and it overcome the difficulties to solve the PDEs. The transformed ordinary differential equations are solved with the help of help of finite element scheme. The obtained solution is plotted against numerous involved parameters and comparative study is established for the reliability of method and accuracy of obtained results. An enhancement in fluid temperature is recorded against magnetic parameter and Eckert number. Also, decline in velocity is recorded for Weissenberg number and concentration is controlled against higher values of Schmidt number. Furthermore, it is recommended that the finite element scheme can be implemented to handle complex coupled nonlinear differential equation arising in modeling of several phenomena occurs in mathematical physics. [ABSTRACT FROM AUTHOR]

Electro-osmotic flow via a microchannel has numerous uses in the contemporary world, including in the biochemical and pharmaceutical industries. This research explores the electroosmotic flow of Casson-type nanofluid with Sodium Alginate nanoparticles through a vertically tilted microchannel. In addition, the transverse magnetic field is also considered. In this flowing fluid, the influence of heat and mass transmission is also explored. The aforementioned physical process is represented by partial differential equations. Utilizing suitable dimensionless variables for nondimensionalized. Furthermore, the non—dimensional classical system is fractionalized with the use of generalized Fourier and Fick's law. Generalizations are made using the Caputo derivative's description. The analytical solution of the velocity, temperature, and concentration profiles is obtained by combining the methods of Laplace and Fourier. Interestingly, the influence of several physical characteristics such as the fractional parameter, Casson fluid parameter, the thermal and mass Grashof numbers, and the zeta potential parameter is displayed. Moreover, the results show that the volume fractional of nanoparticles enhances the rate of heat transfer up to 39.90%, Skin friction up to 38.05%, and Sherwood number up to 11.11%. Also, the angle of inclination enhances the fluid velocity. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids play a significant role in the advancement of thermal characteristics of pure fluids both at experimental and industrial levels. This work explores the mixed convective MHD micropolar hybrid nanofluid flow past a flat surface. The hybrid nanofluid flow is composed of alumina and silver nanoparticles whereas water is used as a base fluid. The plate has placed vertical in a permeable medium with suction and injection effects. Furthermore, viscous dissipation, thermal radiation and Joule heating effects are taken into consideration. Specific similarity variables have been used to convert the set of modeled equations to dimension-free form and then has solved by homotopy analysis method (HAM). It has revealed in this investigation that, fluid motion upsurge with growth in magnetic field effects and mixed convection parameter and decline with higher values of micropolar factor. Micro-rotational velocity of fluid is upsurge with higher values of micropolar factor. Thermal flow behavior is augmenting for expended values of magnetic effects, radiation factor, Eckert number and strength of heat source. The intensification in magnetic strength and mixed convection factors has declined the skin friction and has upsurge with higher values of micropolar parameter. The Nusselt number has increased with the intensification in magnetic effects, radiation factor and Eckert number. [ABSTRACT FROM AUTHOR]

Scientists and researchers are much interested in studying graphene and silver nanoparticles for the enhancement of heat transport due to their extensive variety of applications in different areas of industrial and engineering such as drug delivery, medical devices, ultra-light, excellent electrical conductivity, strong medical strength, health care, consumer, food, etc. Therefore, in the existing investigation, the MHD flow of a mixed convective hybrid nanoliquid with graphene and silver nanoparticles past a rotating disk is considered. Water and ethylene glycol (50:50) is used as a base liquid in the existing model. The mechanism for heat transport is computed with the existence of thermal radiation and thermal convective condition. Homogeneous and heterogeneous chemical reactions are assumed in the flow behavior. The mathematical formulation of the proposed problem is based on the nonlinear PDEs which are then transformed to nonlinear ODEs by manipulating the appropriate similarity transformation. The simulation of the existing problem has been performed with the help of the homotopy analysis technique. The outcomes of the different flow parameters on the velocities, temperature, concentration, skin friction coefficient, and Nusselt number of the hybrid nanofluid are attained via graphs and tables. Some significant results from the existing problem demonstrate that the rate of heat transport is greater for the thermal Biot number and nanoparticles volume fraction. Further, it is noticed that the velocity of the liquid particles becomes lower for a higher magnetic field parameter. [ABSTRACT FROM AUTHOR]

This article aims to study entropy generation and heat transfer due to free convection. Two types of base fluids (water and kerosene oil) are taken with a suspension of titanium alloy nanoparticles. An external magnetic field is applied in a perpendicular direction and the induced magnetic field is neglected. Scientific analysis is performed on magnetohydrodynamic flow through a Darcy medium. Free convection and the sudden motion of the heated plate cause the fluid to flow. The problem is formulated in terms of differential equations with associated physical conditions. Relations for entropy generation and Bejan numbers are also provided. The Laplace transform technique has been used for finding the exact solution to the problem. Results are plotted using Mathcad software and a comparison is made between water-titanium alloy and kerosene oil-titanium alloy nanoparticles for velocity, temperature, entropy generation, and Bejan number. It is concluded that kerosene oil base fluid has a greater velocity and temperature profile in all parametric studies as compared to water-based fluid. While in the case of entropy generation and Bejan number, near to the plate and for away the plate the behaver is distinct. Entropy generation and Bejan number are boosting up via using different base fluid. For larger estimation of Brinkman number, both Bejan number and entropy rate have the opposite effect. The volume fraction of nanofluid enhance the rate of heat transfer in case of both nanofluid. While the water base nanofluid enhance the rate of heat transfer up to 19.14% and kerosene oil base fluid is enhanced up to 30.01%. [ABSTRACT FROM AUTHOR]

This paper provides iterative construction of a common solution associated with a class of equilibrium problems and split convex feasibility problems. In particular, we are interested in the equilibrium problems defined with respect to the pseudomonotone and Lipschitz-type continuous equilibrium problem together with the generalized split null point problems in real Hilbert spaces. We propose an iterative algorithm that combines the hybrid extragradient method with the inertial acceleration method. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under suitable set of constraints and numerical results concerning the viability of the proposed algorithm with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

In this paper we suggest a theoretical framework to study the generalized split null point problem (GSNPP) via a multi-step inertial based parallel hybrid projection algorithm in Hilbert spaces. The architecture and the suitable set of control conditions ensure the strong convergence of the algorithm. The possible applications of the algorithm are illustrated via various theoretical and numerical results. The key advantages of the algorithm are highlighted in comparison to the classical and non-inertial algorithm as well as (one-step and two-step) inertial variants of the algorithm for the GSNPP. [ABSTRACT FROM AUTHOR]

Following to improved thermal impact of hybrid nanomaterials, wide range applications of such materials is observed in the thermal engineering, extrusion systems, solar energy, power generation, heat transfer devices etc. The hybrid nanofluid is a modified form of nanofluid which is beneficial for improving energy transfer efficiency. In current analysis, the solid nanoparticles aluminium ( ϕ Al 2 O 3 ) and copper ( ϕ Cu ) have been mixed with water to produce a new hybrid nanofluid. The investigation of a steady two-dimensional mixed convection boundary layer flow of the resultant hybrid nanofluid on a vertical exponential shrunk surface in the existence of porous, magnetic, thermal radiation, velocity, and thermal slip conditions is carried out. Exponential similarity variables are adopted to transform the nonlinear partial differential equation into a system of ordinary differential equations which has been then solved by employing the shooting method in Maple software. The obtained numerical results such as coefficient of skin friction f ″ 0 , heat transfer rate - θ ′ 0 , velocity f ′ η and temperature θ η distributions are presented in the form of different graphs. The results revealed that duality exists in solution when the suction parameter S ≥ S ci in assisting flow case. Due to non-uniqueness of solutions, a temporal stability analysis needs to be performed and the result indicates that the upper branch is stable and realizable compared to the lower branch. [ABSTRACT FROM AUTHOR]

This report presents the three-dimensional electromagnetohydrodynamic flow of a zinc-oxide–water nanofluid past a bidirectional Riga plate with velocity slips and thermal and mass convection conditions. The Cattaneo–Christov heat and mas flux model, thermal radiation, chemical reaction and activation energy are considered to analyze the flow problem. The volume fraction of the ZnO nanoparticles is taken 6% in this analysis. An appropriate set of similarity variables is used to transform the partial differential equations into ordinary differential equations. During this process, some parameters are found and influences of these factors on the flow profiles are shown and discussed in detail. A numerical technique called NDSolve is considered for the solution of the nanofluid flow problem. The results showed that higher solid volume fraction and slip parameter have reduced velocities profiles and the increasing solid volume fraction and thermal Biot number have increased the temperature profile. Additionally, the concentration Biot number has increased the concentration profile. The modified Hartmann number has significantly increased the velocity profile. Dual impacts in velocity profiles along primary and secondary direction has been observed due to stretching ratio parameter. A comparison of current results has been carried with a fine agreement amongst current and established results. [ABSTRACT FROM AUTHOR]

In this paper, the potential differential game concept introduced by Fonseca-Morales and Hernández-Lerma (2018) is used in analyzing stabilization problems for n-player noncooperative capital accumulation games (CAGs). By first identifying a CAG as a potential game, an associated optimal control problem (OCP) of the CAG is obtained, whose optimal solution is an open-loop Nash equilibrium for the CAG. Compared with a saddle-point stability condition obtained for undiscounted CAG in the literature, a sufficient and easily verifiable condition is obtained for both discounted and undiscounted CAGs. In addition, the concept allows the turnpike property obtained for OCPs in Trélat and Zuazua (2015) to be verified for CAGs. Lastly, an illustrative example is given to verify the latter stability result for some CAGs. [ABSTRACT FROM AUTHOR]

The Jeffrey fluid model is capable of accurately characterizing the stress relaxation behavior of non-Newtonian fluids, which a normal viscous fluid model is unable to perform. The primary objective of this paper is to provide a comprehensive investigation into the effects of MHD and thermal radiation on the 3D Jeffery fluid flow over a permeable irregular stretching surface. The consequences of the Darcy effect, variable thickness and chemical reaction are also considered. The phenomena have been modeled as a nonlinear system of PDEs. Using similarity substitution, the modeled equations are reduced to a dimensionless system of ODEs. The parametric continuation method (PCM) is used to determine the numerical solution to the obtained sets of nonlinear differential equations. The impact of physical parameters on temperature, velocity and mass profiles are presented through Figures and Tables. It has been noticed that the energy profile magnifies with the increment of porosity term, thermal radiation and heat source term, while diminishing with the flourishing upshot of power index and Deborah number. Furthermore, the porosity term and wall thickness parameter enhance the skin friction. [ABSTRACT FROM AUTHOR]

The thermal distribution in a convective-radiative concave porous fin appended to an inclined surface has been examined in this research. The equation governing the temperature and heat variation in fin with internal heat generation is transformed using non-dimensional variables, and the resulting partial differential equation (PDE) is tackled using an analytical scheme, generalized residual power series method (GRPSM). Moreover, a graphical discussion is provided to examine the consequence of diverse non-dimensional variables including the parameters of convection-conduction, ambient temperature, radiation, heat generation, and porosity effect on the thermal field of the fin. Also, a graph is plotted to analyze the variations in unsteady temperature gradient using the finite difference method (FDM) and generalized residual power series method (GRPSM). The major result of this investigation unveils that as the convection-conduction parameter scale upsurges, the distribution of temperature in the fin diminishes. For the heat-generating parameter, the thermal distribution inside the fin increases. [ABSTRACT FROM AUTHOR]

We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the proposed scheme is established under mild assumptions and several synthetic and practical numerical illustrations demonstrate the validity and advantages of our method compared with related schemes in the literature. [ABSTRACT FROM AUTHOR]

The researchers are continuously working on nanomaterials and exploring many multidisciplinary applications in thermal engineering, biomedical and industrial systems. In current problem, the analytical simulations for performed for thermos-migration flow of nanofluid subject to the thermal radiation and porous media. The moving wedge endorsed the flow pattern. The heat source effects are also utilized to improves the heat transfer rate. The applications of thermophoresis phenomenon are addressed. The formulated set of expressions are analytically treated with implementation of variational iteration method (VIM). The simulations are verified by making the comparison the numerical date with existing literature. The VIM analytical can effectively tackle the nonlinear coupled flow system effectively. The physical impact for flow regime due to different parameters is highlighted. Moreover, the numerical outcomes are listed for Nusselt number. [ABSTRACT FROM AUTHOR]

In an infinite-dimensional real Hilbert space setting, we introduce a new self-adaptive inertial Halpern-type projection algorithm for solving multiple-sets split feasibility problem assuming that the involved convex subsets are level subsets of strongly convex functions by approximating the original convex subsets by a sequence of closed balls instead of half-spaces. Since the projection onto the closed ball has a closed form, the proposed algorithm is hence easy to implement. Moreover, we construct a new self-adaptive stepsize that is bounded away from zero and is independent of the operator norm. Under some mild assumptions and without the usual Lipschitz’s continuity of the gradient operator assumption, we establish and prove a strong convergence of the sequence generated by the proposed algorithm. Several numerical illustrations indicate that the proposed algorithm is computationally efficient and competes well with some existing algorithms in the literature. The proposed method is an improvement and generalization of many results in the literature. [ABSTRACT FROM AUTHOR]

The current study is presented to simulate the three-dimensional MHD flow of micropolar and Williamson fluids over an extending sheet. The activation energy and thermal radiation influence are presented in the current investigation. The significance of chemical reaction, Brownian motion, and thermophoresis impacts is also calculated. The present flow problem is developed in the form of highly nonlinear PDEs along with the boundary conditions. Appropriate similarity transformations are considered for the transformations of highly nonlinear PDEs into ODEs. For the simplification of the problem, the most powerful analytical method known as the homotopic analysis technique is utilized. The influences of the dimensionless parameters on the flow profiles are examined. Some significant key results of the present analysis are that the skin friction coefficients are reduced with the enhancement of magnetic field and Williamson fluid parameters. Nusselt number is decayed for the Brownian motion and thermophoresis parameters. The nanoliquid temperature becomes lower for higher Prandtl number. [ABSTRACT FROM AUTHOR]