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Hedonic price modeling (HPM) plays an important role in identifying factors affecting the price of goods or services. Many researchers have extensively used this modeling approach in their research work. However, there has been no bibliometric review that analyses the existing research, which makes use of HPM modeling. This study aims to provide a comprehensive visualized bibliometric and scientometric view of HPM usage in real estate research.

The Scopus database was used to collect the bibliographic data of 269 publications from 1970 to 2019. CiteSpace software was then used to analyze and visualize the data.

The results revealed a significant increase in the annual number of HPM study publications. Core authors, participating countries and representative references have been identified. Research hotspots for the HPM studies were identified.

While the study provides a methodological bibliometric review of HPM literature, the findings provide a very good platform for understanding the important elements of HPM usage in real estate research.

The purpose of this paper is to implement variational iteration method (VIM) and homotopy perturbation method (HPM) to solve modified Camassa‐Holm (mCH) and modified Degasperis‐Procesi (mDP) equations.

Perturbation method is a traditional method depending on a small parameter which is difficult to be found for real‐life nonlinear problems. To overcome the difficulties and limitations of the above method, two new ones have recently been introduced by He, i.e. VIM and HPM. In this paper, mCH and mDP equations are solved through these methods.

To assess the accuracy of the solutions, the comparison of the obtained results with the exact solutions reveals that both methods are tremendously effective.

The paper shows that VIM and HPM can be implemented to solve mCH and mDP equations.

This paper aims to deal with the application of variational iteration method and homotopy perturbation method (HPM) for solving one dimensional shallow water equations with crisp and fuzzy uncertain initial conditions.

Firstly, the study solved shallow water equations using variational iteration method and HPM with constant basin depth and crisp initial conditions. Further, the study considered uncertain initial conditions in terms of fuzzy numbers, which leads the governing equations to fuzzy shallow water equations. Then using cut and parametric concepts the study converts fuzzy shallow water equations to crisp form. Then, HPM has been used to solve the fuzzy shallow water equations.

Results obtained by both methods HPM and variational iteration method are compared graphically in crisp case. Solution of fuzzy shallow water equations by HPM are presented in the form triangular fuzzy number plots.

Shallow water equations with crisp and fuzzy initial conditions have been solved.

The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical solutions of the fractional KdV‐Burgers‐Kuramoto equation.

The authors used Maple Package to calculate the functions obtained from the HPM.

The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.

The paper describes how the HPM has been successfully applied to find the solution of fractional KdV‐Burgers‐Kuramoto equation.

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

Three terms from HPM solution are used.

The results show that this method is very effective and simple and can be applied to other nonlinear problems.

Comparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.

It is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.

In this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

The purpose of this paper is to determine the most significant factors influencing apartment values in Nairobi Metropolitan Area (NMA), Kenya and develop a valuation model using the identified variables. The paper is thus promoting the adoption of advanced, more reliable and accurate valuation methods in developing economies such as Kenya. Therefore, the paper demonstrates the potential of the hedonic pricing method (HPM) in property valuation by making objective adjustments to comparable sales data.

The paper utilizes a case study design by analysing recent (January 2020 to December 2021) apartment sales and apartment attributes in NMA. A sample size of 264 transactions was analysed using the HPM.

The study identified six significant factors affecting apartment values in the study area: apartment size, location, floor finishes, provision of shopping facilities, swimming pool and gym. A valuation model has been developed using the six variables.

The paper is contributing to the ongoing global debate on the accuracy, reliability and validity of property valuations with particular emphasis on the developing economies to adopt the more accurate, efficient and reliable valuation approaches.

The findings are useful to property valuers and estate managers in determining the most statistically significant attributes affecting apartment values in the NMA hence enabling them to offer informed professional advice. However, the findings of the study are limited to the study area since real estate is heterogeneous.

Property investors, financiers and other stakeholders in the society will benefit from the findings of this study in their decision-making process. Additionally, wide adoption of the more reliable and accurate valuation approaches would foster public confidence in valuation and estate management professional services leading to enhanced consumption of these services by the society and promoting public care.

The paper is promoting valuation accuracy, efficiency and reliability in the developing economies by advocating for advanced valuation methods. It is the first attempt to develop a valuation model for apartments in the NMA, the capital city of Kenya and the business hub of East and Central Africa.

The purpose of this paper is to introduce a new homotopy perturbation method (NHPM) to solve Cauchy problem of unidimensional non‐linear diffusion equation.

In this paper a modified version of HPM, which the authors call NHPM, has been presented; this technique performs much better than the HPM. HPM and NHPM start by considering a homotopy, and the solution of the problem under study is assumed to be as the summation of a power series in p, the difference between two methods starts from the form of initial approximation of the solution.

In this article, the authors have applied the NHPM for solving nonlinear Cauchy diffusion equation. In comparison with the homotopy perturbation method (HPM), in the present method, the authors achieve exact solutions while HPM does not lead to exact solutions. The authors believe that the new method is a promising technique in finding the exact solutions for a wide variety of mathematical problems.

The basic idea described in this paper is expected to be further employed to solve other functional equations.

This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation.

Using HPM the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. Also, by using VIM the analytical results of this equation have been obtained in terms of convergent series with easily computable components.

Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy.

Also the results show that the introduced methods are efficient tools for solving the nonlinear partial differential equations.

The purpose of this paper is to present a general framework of Homotopy perturbation method (HPM) for analytic inverse heat source problems.

The proposed numerical technique is based on HPM to determine a heat source in the parabolic heat equation using the usual conditions. Then this shows the pertinent features of the technique in inverse problems.

Using this HPM, a rapid convergent sequence which tends to the exact solution of the problem can be obtained. And the HPM does not require the discretization of the inverse problems. So HPM is a powerful and efficient technique in finding exact and approximate solutions without dispersing the inverse problems.

The essential idea of this method is to introduce a homotopy parameter p which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

The purpose of this paper is to report the effect of radiation on flow of a magneto‐micropolar fluid past a continuously moving plate with suction and blowing.

The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely the homotopy perturbation method (HPM) combining with Padé approximants and finite difference method, are used to solve dimensionless non‐linear ordinary differential equations. The skin friction coefficient and local Nusselt numbers are also calculated. Beside this, the comparison of the analytical solution with numerical solution is illustrated by the graphs for different values of dimensionless pertinent parameters.

The authors have studied laminar magneto‐micropolar flow in the presence of radiation by using HPM‐Padé and finite difference methods. Results obtained by HPM‐Padé are in excellent agreement with the results of numerical solution.

The HPM‐Padé is used in a direct way without using linearization, discritization or restrictive assumption. The authors have attempted to show the capabilities and wide‐range applications of the HPM‐Padé in comparison with the finite difference solution of magneto‐micropolar flow in the presence of radiation problem.