Search

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced. [ABSTRACT FROM AUTHOR]

The current communication has as its goal the investigation of the flow properties of carbon nanotubes (CNTs) across a stretching surface, which has been accomplished. Furthermore, the effects of radiation, chemical reactions and activation energy are considered. With the use of boundary layer approximations, we can obtain flow expressions. The nondimensional form of flow equations is achieved by applying appropriate transformations. The bvp4c code from MATLAB is used to solve the model that has been obtained. The graphic representation of the relationship between pertinent variables and momentum, temperature field and concentration is used. It is observed that, for larger values of ϕ booms, the micro-rotation distribution. Furthermore, the solutal boundary layer thickness if thinner for thicker values of σ. [ABSTRACT FROM AUTHOR]

In this paper, we examine the time-dependent two-dimensional cable equation of fractional order in terms of the Caputo fractional derivative. This cable equation plays a vital role in diverse areas of electrophysiology and modeling neuronal dynamics. This paper conveys a precise semi-analytical method called the q-homotopy analysis transform method to solve the fractional cable equation. The proposed method is based on the conjunction of the q-homotopy analysis method and Laplace transform. We explained the uniqueness of the solution produced by the suggested method with the help of Banach’s fixed-point theory. The results obtained through the considered method are in the form of a series solution, and they converge rapidly. The obtained outcomes were in good agreement with the exact solution and are discussed through the 3D plots and graphs that express the physical representation of the considered equation. It shows that the proposed technique used here is reliable, well-organized and effective in analyzing the considered non-homogeneous fractional differential equations arising in various branches of science and engineering. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips' impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both e 1 and ε parameters. [ABSTRACT FROM AUTHOR]

AbstractThis research looks at the flow of hybrid nanoparticles across a wedge-shaped surface. In addition to this, Brownian motion and thermal stratification are used to model how heat moves through a system. The mass expression also deals with the thermophoresis effect and mass stratification. The governing equations involve the continuity, momentum, energy, and mass equation of hybrid nanofluids that are modified into ODE's by applying similarity transformation. The solutions are obtained from two well-known numerical routines, RKF-45 and the profiles embodying f′(η),θ(η), and P(η) are interpreted under the influence of several physical parameters. The results showed that as the Prandtl number goes up, temperature profiles of fluid flow go down, and as Brownian motion factors go up, temperature profiles go up. It is found that the fluid’s thermal flow rate slows down as the Brownian motion and thermophoretic elements get stronger. On the other hand, the thermal flow rate of fluid goes up as the thermal stratification parameter goes up. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present study is to find the solution for a nonlinear system describing the aggregation process of cellular slime mold by using q -homotopy analysis transform method. The coupled system is considered within the frame of the Caputo fractional operator. We examine three different cases with distinct values of sensitivity function χ ρ = 1 , ρ and ρ 2 to exemplify the efficiency and applicability of the considered scheme. We capture the nature of the obtained results with respect to the fractional order, with distinct initial conditions, and illustrate them using 2D and 3D plots for particular values of the parameters. The considered scheme offers parameters, which help to adjust the convergence region, and we plotted the ℏ-curves to dissipate the effect in the present framework. Moreover, some simulating and important behavior of the considered model using attained results shows the prominence of the hired operator while analyzing the coupled equations and confirms the competence of the projected scheme. [ABSTRACT FROM AUTHOR]

This study looks at the impact of a magnetic dipole on swirling flow and heat transmission over a deformable cylinder. This model considers the impacts of alumina alloys nanoparticles as well as linear radiation in (AA7075 and AA7072) viscous nanofluids-based-H2O. The Navier–Stokes equation was utilized to express the predicted flow quantitatively. The partial differential equations (PDEs) required to investigate the flow assumptions were created using the boundary layer approximation of the Navier–Stokes equation. The ordinary differential equations (ODEs) formalism can be employed by modifying the system with similar conversions. The bvp4c methodology is employed to describe a system with no dimensions. The numerical and graphical representations of the data provide a clear understanding of the roles played by the essential physical constituents. The results showed that the increment in aluminium alloys nanoparticles reduces the surface frictional forces, while the incrementation in the magnetic interaction parameter improves the heat transfer of the nanofluid. [ABSTRACT FROM AUTHOR]

This paper presents the study of time-fractional nonlinear fifth-order Korteweg–de Vries equations by utilizing an adequate novel technique, namely, the q-homotopy analysis transform method. The fifth-order Korteweg–de Vries equation has got its importance in the study of magneto-sound propagation in plasma, capillary gravity water waves, and the motion of long waves under the influence of gravity in shallow water. To justify the effectiveness and pertinence of the contemplated technique, we take a look at three examples of the time-fractional fifth-order Korteweg–de Vries equations. The q-homotopy analysis transform method offers us to modulate the range of convergence of the series solution using ℏ, called the auxiliary parameter or convergence control parameter. The study of the fractional behaviour of the considered equations expresses the originality of the presented work. There is a visible variation in the obtained solutions for different fractional orders and which can lead to different consequences for future work. As a future research direction, readers can use the hybrid methodologies merging with our projected scheme to achieve better consequences. Additionally, to validate the precision and reliability of the proposed method, we organized suitable numerical simulations. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation. [ABSTRACT FROM AUTHOR]

Squeezing flow of Casson liquid between two disks is a practical application in compression, polymer processing and injection molding. In this paper, the Casson liquid flow between two convectively heated disks is analyzed using Buongiorno model. Further, the heat and mass transport analysis is done by considering the impact of heat source/sink and activation energy. The continuity and momentum equations governing the unsteady two-dimensional flow are derived using conservative laws. The equations are reformulated using the similarity transformations and the reformulated equations are solved numerically with MATLAB routine bvp4c. The effect of embedding different physical parameters on the flow is analyzed through the graphs for both suction and blowing cases along with comprehensive solutions and equal Biot numbers. Results are validated with the existing literature. For both suction and blowing cases, squeezing number decreases the velocity near the lower disk but increases the velocity near the upper disk. Increasing magnetic field strength slightly increases velocity near the lower disk for equal Biot numbers. [ABSTRACT FROM AUTHOR]

In this note, the generalized Lorentzian Sasakian-space-form M 1 2 n + 1 (f 1 , f 2 , f 3) satisfying certain constraints on the M -projective curvature tensor W * is considered. Here, we characterize the structure M 1 2 n + 1 (f 1 , f 2 , f 3) when it is, respectively, M -projectively flat, M -projectively semisymmetric, M -projectively pseudosymmetric, and φ − M -projectively semisymmetric. Moreover, M 1 2 n + 1 (f 1 , f 2 , f 3) satisfies the conditions W * (ζ , V 1) · S = 0 , W * (ζ , V 1) · R = 0 and W * (ζ , V 1) · W * = 0 are also examined. Finally, illustrative examples are given for obtained results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds. First, we show that if a K -paracontact manifold M 2 n + 1 is the spatial factor of a static perfect fluid space-time, then M 2 n + 1 is of constant scalar curvature − 2 n (2 n + 1) and squared norm of the Ricci operator is given by 4 n 2 (2 n + 1). Next, we prove that if a (κ , μ) -paracontact metric manifold M 2 n + 1 with κ > − 1 is a spatial factor of static perfect space-time, then for n = 1 , M 2 n + 1 is flat, and for n > 1 , M 2 n + 1 is locally isometric to the product of a flat (n + 1) -dimensional manifold and an n -dimensional manifold of constant negative curvature − 4. Further, we prove that if a paracontact metric 3-manifold M 3 with Q ϕ = ϕ Q is a spatial factor of static perfect space-time, then M 3 is an Einstein manifold. Finally, a suitable example has been constructed to show the existence of static perfect fluid space-time on paracontact metric manifold. [ABSTRACT FROM AUTHOR]

The main goal of this study is to find solutions for the generalized coupled Ramani equation with the fractional order using the fractional natural decomposition method (FNDM). Four distinct cases are chosen to illustrate and validate the effectiveness of the considered method. The simulations in terms of numeric have been illustrated to confirm the reliability and proficiency of the projected scheme. Moreover, the behavior of the obtained results is captured for distinct fractional order. The comparison study is illustrated to verify the accuracy of the projected procedure. The achieved results exemplify that the projected solution procedure offers a simple algorithm and is also very efficient to analyze the nature of the coupled differential equations with arbitrary order situated in associated areas of Science and Engineering. [ABSTRACT FROM AUTHOR]

In present work, we investigate the numerical solution of time-fractional Jaulent–Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transform method (CFRDTM) and q-homotopy analysis transform method (q-HATM). The obtained solutions are presented in a series form, which are converges rapidly. In order to verify the proposed techniques are reliable and accurate, the numerical simulations have been conducted in terms of absolute error. The obtained solutions are presented graphically to ensure the applicability and validity of the considered algorithms. The results of the study reveal that, the q-HATM is computationally very effective and accurate as compared to CFRDTM to analyse fractional nonlinear coupled JM equations. [ABSTRACT FROM AUTHOR]

A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed with Atangana–Baleanu (AB) operator, and the technique we consider is a mixture of the q-homotopy analysis scheme and the Laplace transform. The fixed point hypothesis is considered for the existence and uniqueness of the obtained solution of this model. For the validation and effectiveness of the projected scheme, we analyse the FEFK equation in terms of arbitrary order for the two distinct cases. Moreover, numerical simulation is demonstrated, and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured. [ABSTRACT FROM AUTHOR]

In this paper we study the nature of Ricci solitons in a hyper generalized pseudosymmetric D-homothetically deformed Kenmotsu manifold. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present work is to obtain an approximated analytical solution for the fractional smoking epidemic model with the aid of a novel technique called q-homotopy analysis transform method (q-HATM). The considered nonlinear mathematical model has been effectively employed to elucidate the evolution of smoking in a population and its impact on public health in a community. We find some new approximate solutions in a series form, which converges rapidly, and the proposed algorithm provides auxiliary parameters, which are very reliable and feasible in controlling the convergence of obtained approximate solutions. Further, we present novel simulations for all cases of results to validate the applicability and effectiveness of proposed scheme. The outcomes of the study reveal that the q-HATM is computationally very effective to analyse nonlinear fractional differential equations arises in daily life problems. [ABSTRACT FROM AUTHOR]

In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, q -HATM), is applied to nonlinear Fisher's equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters ħ and n , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the q -HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we apply the q -homotopy analysis transform method to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional. We find some new approximate numerical results for different values of parameters of alpha. Then, we present novel simulations for all cases of results conducted by considering the values of parameters of alpha in terms of two- and three-dimensional figures along with tables including critical numerical values. [ABSTRACT FROM AUTHOR]

The paper deals with the study of M-projective curvature tensor on (κ, μ)-contact metric manifolds. We classify non-Sasakian (κ, μ)-contact metric manifold satisfying the conditions R(ξ,X) ·M = 0 and M(ξ,X) · S = 0, where R and S are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a (κ, μ)-contact metric manifold with vanishing extended M-projective curvature tensor Me is a Sasakian manifold. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study weakly symmetries of Kenmotsu manifolds with respect to quarter-symmetric metric connection. We investigate the properties of weakly symmetric, weakly Ricci-symmetric and weakly concircular Ricci-symmetric Kenmotsu manifolds with respect to quarter symmetric metric connection and obtain interesting results. [ABSTRACT FROM AUTHOR]

The object of this paper is to study (k, µ)-para contact metric manifolds with qusi-conformal curvature tensor. It has been shown that, h-quasi conformally semi-symmetric and φ-quasi-conformally semi-symmetric (k, µ)-paracontact metric manifold with k ≠ - 1 cannot be an η-Einstein manifold. [ABSTRACT FROM AUTHOR]

The present paper deals with a study of 3-dimensional contact metric generalized (κ, μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized (κ, μ)-space form with Q... = ...Q to be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric and ξ-projectively flat, respectively. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study generalized ϕ-recurrent Lorentzian α-Sasakian manifolds. [ABSTRACT FROM AUTHOR]

In this paper we study the conservative conformal curvature tensor and the conservative quasi-conformal curvature tensor on a trans-Sasakian manifold with respect to a semi-symmetric metric connection. It is shown that a trans-Sasakian manifold with conservative conformal curvature tensor is an Einstein manifold, and with quasi-conformal curvature tensor is an η-Einstein manifold. [ABSTRACT FROM AUTHOR]

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using q -homotopy analysis transform method (q -HATM). The considered scheme is a unification of q -homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems. [ABSTRACT FROM AUTHOR]

In the present investigation, the q-homotopy analysis transform method (q-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions and the exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution. [ABSTRACT FROM AUTHOR]

In this paper we study NMCP manifolds, which are (2p+2q+2)--dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the *--Ricci tensor. We prove that a *--Ricci-semi-symmetric NMCP manifold is *--Ricci-flat, and that a *--generalized quasi-Einstein NMCP manifold cannot be *--Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space. [ABSTRACT FROM AUTHOR]

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely the q-homotopy analysis transform method. These equations play a vital role in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis are presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis is discussed to verify the accuracy. The numerical simulation is conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are presented, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arising in science and technology. [ABSTRACT FROM AUTHOR]

This work proposes a semi-analytical new hybrid approach, so-called differential -transform method (D TM), to evaluate the behavior of n-space dimensional fractional-nonlinear hyperbolic-like wave equations, where time-fractional derivative is considered in Caputo format. The D TM is the hybrid method in which projected differential transform is implemented after imposing the recently introduced integral transform, i.e., so-called transform [W. Zhao and S. Maitama, J. Appl. Anal. Comput. 10, 1223 (2020)]. The efficiency and applicability of the proposed D TM had been tested by considering three different test examples of the Caputo time-fractional nonlinear hyperbolic-like wave equations in terms of absolute error norms, and the different order D TM solutions are compared with exact solution behaviors and the existing results, for the large time level τ ∈ [ 0 , 1 0 ]. In addition, the convergence analysis of D TM is studied theoretically and verified it numerically as well as graphically, which confirms that the numerical experiments via D TM for distinct fractional orders support the theoretical findings excellently, and the presented D TM results converge to their exact solution behavior, very fast. The evaluated series approximations are expressed in the compact form of Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with q -homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering. [ABSTRACT FROM AUTHOR]

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant φ-sectional curvature, and prove the structure theorem for ξ-conformally flat and φ-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an η-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature ε. [ABSTRACT FROM AUTHOR]

The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis J -transform method ( O HA J TM) and J -variational iteration transform method (J -VITM) have been adopted. The OHA J TM is the hybrid method, where optimal-homotopy analysis method ( O HAM) is utilized after implementing the properties of J -transform (J T), and in J -VITM is the J -transform-based variational iteration method. Banach's fixed point approach is adopted to analyze the convergence of these methods. It is demonstrated that J -VITM is T -stable, and the evaluated dynamics of pGas are described in terms of Mittag–Leffler functions. The proposed evaluation confirms that the implemented methods perform better for the referred model equation of pGas. In addition, for a given iteration, the proposed behavior via O HA J TM performs better in producing more accurate behavior in comparison to J -VITM and the methods introduced recently. [ABSTRACT FROM AUTHOR]

The flow of fluid that occurs when two parallel disks are squeezed together has applications in compression, the processing of polymers, the production of plastics, injection modeling, and lubrication systems. In this paper, the unsteady squeezing flow and heat transport of nanoliquid that is subjected to convective thermal boundary conditions and viscous heating have been studied numerically. This study was inspired by the exploration of the thermophysical properties of magnetic nanoparticles in squeezing tribology. The flow between two horizontal parallel disks is accounted for where the upper disk is non-static when the lower disk is fixed. The powerful Runge–Kutta method-based shooting scheme is utilized to solve the assumed problem. The influence of pertinent key parameters on involved fields is visualized graphically and scrutinized. It is exhibited that the haphazard motion of NPs contributes highly to the enhancement of thermal and concentration fields. Also, the Robin boundary conditions affect flow fields significantly. Intensifying the Brownian motion effect enhances NPs' concentration. Radial velocity is damped in the core region with stronger magnetic field. The mass transport rate is diminished, and the heat transmission rate is enhanced. The computations are relevant to smart nano-tribological systems in mechanical and aerospace engineering. [ABSTRACT FROM AUTHOR]

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China. [ABSTRACT FROM AUTHOR]

In this paper, a solution of coupled fractional Navier–Stokes equation is computed numerically using the proposed q-homotopy analysis transform method (q-HATM), and the solution is found in fast convergent series. The given test examples illustrate the leverage and effectiveness of the proposed technique. The obtained results are demonstrated graphically. The present method handles the series solution in a large admissible domain in an extreme manner. It offers us a modest way to adjust the convergence region of the solution. Results with graphs explicitly reveal the efficiency and capability of the proposed algorithm. [ABSTRACT FROM AUTHOR]