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Leadership literature has identified that the servant leadership style can reduce employee negative work outcomes, even in challenging work environments like the health-care sector as nurses play an important role in the performance of a hospital. That is why, the efficiency and effectiveness of the nurses are believed to be directly linked to improved health benefits to the public. So, this study aims to investigate the inter-relationship between servant leadership, organizational justice and workplace deviance of nurses in public sector hospitals.

A self-administrated questionnaire using a drop-and-collect method was used for collecting the data from nurses working in the public sector hospitals of Pakistan using a convenient sampling technique. In total, 370 questionnaires were distributed among the nursing staff, of which 201 completed and usable questionnaires were returned and used for data analysis. Further, the partial least squares structural equation modeling approach is used in this study using SmartPLS version 3 software to test the hypothesized model and determine the direct and indirect effects.

Results showed a negative relationship between servant leadership and workplace deviance, positive relationship between servant leadership and organizational justice, negative relationship between organizational justice and workplace deviance and that organizational justice mediates in the relationship between servant leadership and workplace deviance.

This study provides valuable recommendations and practical implications to address the nurses’ deviant workplace behaviors in the public sector hospitals of Pakistan.

This study is novel as it shows the significance of servant leadership behavior which has the ability to positively influence organizational justice perception leading to less likelihood of the emergence of nurses’ deviant workplace behavior, specifically in the context of public sector hospitals of Pakistan.

In the nonlinear model of reaction–diffusion, the Fitzhugh–Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh–Nagumo equation through the use of variational formulation.

The partial differential equation of Fitzhugh–Nagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi-inverse variational method.

This paper uses a variational approach to the Fitzhugh–Nagumo equation developing new solitary solutions. The condition for the continuation of new solitary solutions has been met. In addition, this paper sets out the Fitzhugh–Nagumo equation fractal model and its variational principle. The findings of the solitary solutions have shown that the suggested method is very reliable and efficient. The suggested algorithm is very effective and is almost ideal for use in such problems.

The Fitzhugh–Nagumo equation is an important nonlinear equation for reaction–diffusion and is typically used for modeling nerve impulses transmission. The Fitzhugh–Nagumo equation is reduced to the real Newell–Whitehead equation if β = −1. This study provides researchers with an extremely useful source of information in this area.

This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM).

The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs.

It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number.

To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

Nizhnik–Novikov–Veselov system (NNVS) is a well-known isotropic extension of the Lax (1 + 1) dimensional Korteweg-deVries equation that is also used as a paradigm for an incompressible fluid. The purpose of this paper is to present a fractal model of the NNVS based on the Hausdorff fractal derivative fundamental concept.

A two-scale transformation is used to convert the proposed fractal model into regular NNVS. The variational strategy of well-known Chinese scientist Prof. Ji Huan He is used to generate bright and exponential soliton solutions for the proposed fractal system.

The NNV fractal model and its variational principle are introduced in this paper. Solitons are created with a variety of restriction interactions that must all be applied equally. Finally, the three-dimensional diagrams are displayed using an appropriate range of physical parameters. The results of the solitary solutions demonstrated that the suggested method is very accurate and effective. The proposed methodology is extremely useful and nearly preferable for use in such problems.

The research study of the soliton theory has already played a pioneering role in modern nonlinear science. It is widely used in many natural sciences, including communication, biology, chemistry and mathematics, as well as almost all branches of physics, including nonlinear optics, plasma physics, fluid dynamics, condensed matter physics and field theory, among others. As a result, while constructing possible soliton solutions to a nonlinear NNV model arising from the field of an incompressible fluid is a popular topic, solving nonlinear fluid mechanics problems is significantly more difficult than solving linear ones.

To the best of the authors’ knowledge, for the first time in the literature, this study presents Prof. Ji Huan He's variational algorithm for finding and studying solitary solutions of the fractal NNV model. The reported solutions are novel and present a valuable addition to the literature in soliton theory.

The purpose of this paper is to investigate the circuit analysis differential equations, which play an important role in the field of electrical and electronic engineering, and it was necessary to propose a very simple and direct method to obtain approximate solutions for the linear or non-linear differential equations, which should be simple for engineers to understand.

This paper introduces a simple novel Maclaurin series method (MSM) to propose an approximate novel solution in the area of circuit analysis for linear and non-linear differential equations. These equations describe the alternating current circuit of the resistor–capacitor, which evaluates the effect of non-linear current resistance. Linear and non-linear differential equations are evaluated as a computational analysis to assist the research, which reveals that the MSM is incredibly simple and effective.

Simulation findings indicate that the achieved proposed solution using the novel suggested approach is identical to the exact solutions mentioned in the literature. As the Maclaurin series is available to all non-mathematicians, this paper reflects mostly on theoretical implementations of the numerous circuit problems that occur in the field of electrical engineering.

A very simple and efficient method has been proposed in this paper, which is very easy to understand for even non-mathematicians such as engineers. The paper introduced a method of the Maclaurin series to solve non-linear differential equations resulting from the study of the circuits. The MSM mentioned here will be a useful tool in areas of physical and engineering anywhere the problem of the circuits is studied.

The purpose of this paper is to present an analytical approximate solution of the nonlinear mathematical model of the bifilar pendulum.

First, the equation of motion derived based on the classical dynamics law by only an angular oscillation assumption and vertical oscillation is neglected. The energy balance method is applied to solve an established model and an analytical formulation has been obtained for the nonlinear frequency of the bifilar pendulum.

A comparison of results with those obtained by a numerical solution of the exact model (without any simplifications) shows the precise accuracy even for a large amplitude of oscillation.

The proposed model and solution are relatively simple and can be applied instead to a linear model for achieving accurate results.

The nonlinear Schrödinger equation plays a vital role in wave mechanics and nonlinear optics. The purpose of this paper is the fractal paradigm of the nonlinear Schrödinger equation for the calculation of novel solitary solutions through the variational principle.

Appropriate traveling wave transform is used to convert a partial differential equation into a dimensionless nonlinear ordinary differential equation that is handled by a semi-inverse variational technique.

This paper sets out the Schrödinger equation fractal model and its variational principle. The results of the solitary solutions have shown that the proposed approach is very accurate and effective and is almost suitable for use in such problems.

Nonlinear Schrödinger equation is an important application of a variety of various situations in nonlinear science and physics, such as photonics, the theory of superfluidity, quantum gravity, quantum mechanics, plasma physics, neutron diffraction, nonlinear optics, fiber-optic communication, capillary fluids, Bose–Einstein condensation, magma transport and open quantum systems.

The variational principle of the Schrödinger equation without the Lagrange multiplier method in the sense of the fractal calculus is developed for the first time in the literature to the best of the author's understanding.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

To explore the fusion of dust particles and of polymers in a viscous liquid is the main purpose of this article. Newtonian fluid as a base fluid is considered and the mutual presence of polymers and dusty bodies is investigated. It discusses the steady laminar flow and heat transportation of a polymeric dusty liquid induced by a uniformly heated, penetrable and stretchable surface inside the boundary layer.

The mathematical system incorporates separate equations of energy and momentum for dusty bodies and for fluid. The classical Oldroyd-B model is chosen for exploring polymer presence. For the fluid phase, this model adds another stress to the conservation law of momentum. Appropriate similarity variables are introduced to transform the system of partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). The problem is solved by introducing a numerical iterative procedure which turned out to be fastly converging.

Expeditious changes inside the boundary layer cause polymers to deform. No changes outside the boundary layer are noticed on account of polymer stretching. The dependence of heat transfer rate and skin friction on the parameter of polymer concentration and Weissenberg number is analyzed and displayed graphically against interaction parameters for temperature and velocity, dust particles’ mass concentration, Eckert and Prandtl numbers. Combining effects of polymers and dust particles cause skin friction to decrease and heat transfer rate to increase. Increasing values of interaction parameter for velocity, dust particles’ mass concentration and Eckert number reduces the drag coefficient and local Nusselt number. On the other hand, the Prandtl number and interaction parameter of temperature magnify the heat flux at the wall.

This article studies the infinite extensibility of polymers. FENE and FENE-P models can be used to investigate the polymer presence in dusty fluids in the future.

In this article, the authors’ aim is to study the combined presence of polymers and dusty bodies. Keeping the existing literature in view, this type of fusion is not studied yet. Polymer inclusion in a viscous dusty fluid is studied and the behavior of fluid flow and heat transportation is investigated within the boundary layer over a permeable linearly stretching sheet.

The purpose of this study is to develop an extended theory of planned behavior (TPB) model by adding religious commitment (RC) and self-efficacy as internal variables and investigating the effect of these variables on attitudes toward halal cosmetics. In addition, this study also examined the moderating role of halal literacy in the relationships between attitudes (ATT), subjective norms (SN), perceived behavioral control (PBC) and intentions to purchase halal cosmetics.

The method of data collection used was self-administered surveys with customers in two stores in Karachi, Pakistan, yielding 267 valid questionnaires. To guarantee validity and reliability, convergent and discriminant validity analyses were conducted, and structural equation modeling was advanced to assess the relationships between variables using smart partial least squares 3.0 software. The interaction moderation technique has been used to examine the moderating effect of halal literacy on the purchase intention (PI) of halal cosmetics.

The results show that RC and self-efficacy both significantly impact the attitudes of Gen Y. Normative beliefs also had a significant relationship with SN. Further, ATT and SN had a significant relationship with PI of halal cosmetics, while PBC was nonsignificant. Furthermore, halal literacy is found to have a positive moderating influence on ATT and PI, and SN and PI. Finally, the moderating effect of halal literacy does not exist in the relationship between PBC and PI.

Participants’ characteristics should vary for future studies, and larger sample sizes may yield different results. It is critical for managers working in the cosmetic industry to monitor Muslim consumption patterns to develop strategies to reach Muslim consumers. This study reveals the effect of RC, self-efficacy and the moderating role of halal literacy on the behavioral attitudes of a booming market sector, which can guide marketing managers in developing more effective advertising campaigns.

This paper contributes to the halal consumption literature by exploring RC and self-efficacy as constructs for the very first time in the TPB model. To the best of the authors’ knowledge, this study is the first to explore the influence of halal literacy on Gen Y Pakistani Muslim consumer behavioral intention toward halal cosmetic products using the TPB model. The paper offers an extended TPB model framework that may be of interest to scholars, marketers and policymakers.