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The purpose of this paper is to solve an unsteady nonlinear convective‐radiative equation and a nonlinear convective‐radiative‐conduction equation containing two small parameters of ε₁ and ε₂ by variational homotopy perturbation method.

The heat transfer equations are described. The variational homotopy perturbation method as a powerful method for solving linear and nonlinear equations is applied to find the solutions of our model equations.

The solutions of heat transfer equations are calculated in the form of convergent series with easily computable components. Two examples are solved as illustrations, using symbolic computation.

The results show that the suggested method is easy to implement and has high level of accuracy. The method introduces a reliable tool for solving many linear and nonlinear differential equations.

The purpose of this paper is to apply an efficient semi-analytical method for the approximate solution of Lienard’s equation of fractional order.

A Laplace decomposition method (LDM) is implemented for the nonlinear fractional Lienard’s equation that is complemented with initial conditions. The nonlinear term is decomposed and then a recursive algorithm is constructed for the determination of the proposed infinite series solution.

A number of examples are tested to explicate the efficiency of the proposed technique. The results confirm that this approach is convergent and highly accurate by using only few iterations of the proposed scheme.

The approach is original and is of value because it is the first time that this approach is used successfully to tackle fractional differential equations, which are of great interest for authors in the recent years.

Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus.

This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given.

Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations.

Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.

The purpose of this paper is to solve an initial-value problem for the general fractional differential equation of the nonlinear Lienard's equation.

A new recursive scheme is presented by combining the Adomian decomposition method with a magnificent recurrence formula and via the solutions of the well-known generalized Abel equation.

It is shown that the proposed method may offer advantages in computing the components yn; n = 1; 2; … in an easily computed formula. Also, the numerical experiments show that with few iterations of the recursive method, this technique converges swiftly and accurately.

The approach is original, and a reasonably accurate solution can be achieved with only two components. Moreover, the proposed method can be applied to several nonlinear models in science and engineering.

Utilizing data from the 2017 Chinese General Social Survey (CGSS2017), the paper aims to investigate the impact of information and communication technology (ICT) adoption on residents' self-rated health and reveals the mechanisms behind ICT.

In the study, ICT adoption is defined as a dummy variable, which takes the value of one if respondents adopt the computers or mobile phone. Meanwhile, respondents' perceptions on five categories of self-rated health are used to construct the dependent variable. Then, based on a fixed-effects regression model, the ordinary least squares (OLS) and ordered probit approaches are applied to estimate their association. Moreover, the two-stage least squares (2SLS) and instrumental variable (IV)-oprobit methods are used to tackle the potential endogeneity of ICT adoption. Finally, the heterogeneity across individuals and regions as well as the underlying mechanisms are discussed.

The results indicate that ICT adoption significantly improves residents' self-rated health, which confirms the health utility model with ICT adoption. The conclusion is robust after overcoming the endogeneity issues with IV. In addition, heterogeneity analysis shows that ICT adoption is more beneficial to the health of residents who are male, young, better educated and those who live in the rural areas and in central and western China. Furthermore, the study demonstrates that ICT adoption for searching health-related information and improving social capital are two crucial mechanisms underlying its health effects.

The findings of this research can help Chinese Government improve population health by issuing corresponding digital and health policies at the regional and individual level.

First, the study provides fresh microscopic evidence on health outcomes of ICT adoption based on data from the latest wave of CGSS2017. Second, individual and regional heterogeneity is extensively discussed in contrast to most related macro studies that consider average effects. Third, the study addresses underlying mechanisms that have not been thoroughly tested or studied primarily on a theoretical level.

The purpose of this paper is to suggest the solution of time-fractional Fornberg–Whitham and time-fractional Fokker–Planck equations by using a novel approach.

First, some basic properties of fractional derivatives are defined to construct a novel approach. Second, modified Laplace homotopy perturbation method (HPM) is constructed which yields to a direct approach. Third, two numerical examples are presented to show the accuracy of this derived method and graphically results showed that this method is very effective. Finally, convergence of HPM is proved strictly with detail.

It is not necessary to consider any type of assumptions and hypothesis for the development of this approach. Thus, the suggested method becomes very simple and a better approach for the solution of time-fractional differential equations.

Although many analytical methods for the solution of fractional partial differential equations are presented in the literature. This novel approach demonstrates that the proposed approach can be applied directly without any kind of assumptions.

The position/force control of the robot needs the parameters of the impedance model and generates the desired position from the contact force in the environment. When the environment is unknown, learning algorithms are needed to estimate both the desired force and the parameters of the impedance model.

In this paper, the authors use reinforcement learning to learn only the desired force, then they use proportional-integral-derivative admittance control to generate the desired position. The results of the experiment are presented to verify their approach.

The position error is minimized without knowing the environment or the impedance parameters. Another advantage of this simplified position/force control is that the transformation of the Cartesian space to the joint space by inverse kinematics is avoided by the feedback control mechanism. The stability of the closed-loop system is proven.

The position error is minimized without knowing the environment or the impedance parameters. The stability of the closed-loop system is proven.

The purpose of this paper is to validate the variational iteration method (VIM) is suitable for various nonlinear equations.

The He’s VIM is applied to solve nonlinear equation which is derived from actual engineering problem. The result was compared with other method.

The result obtained from VIM shows good agreement with Xu’s result which provide a solid evidence that VIM is convenient and effective for solving nonlinear equation in the engineering.

The VIM can be extended to many academic and engineering fields for nonlinear equations solving.

The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system (FFLS) with no non negative restrictions on the triangular fuzzy numbers chosen as parameters. Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions. The first method eliminates the non‐negativity constraint from the coefficient matrix while the second method eliminates the constraint of non‐negativity on the solution vector. The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.

The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system. Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.

The results that are obtained reveal interesting properties of a FFLS. By using the proposed methods, the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions, i.e. trivial, unique or infinite. Further it is also seen that an n×n FFLS may yield finitely many solutions which may not be entirely feasible (strong). Also the methods successfully remove the non‐negativity restriction on the coefficient matrix and the solution vector, respectively.

Evolving methods with better computational complexity and that which remove the non‐negativity restriction jointly on all the parameters are left as an open problem.

The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists. The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations. Heretofore, the usability of FFLS is largely dormant.

The purpose of this paper is to investigate the influences of the interactions of taste, colour and labelling on sensory perception, liking and identification of saffroned products.

The consumer and discrimination tests (N=120, 18, 25, 78, for Experiments 1–4, respectively) were conducted. The analyses of discrimination tests were performed using the Thurstonian model and R-index. The results from consumer studies were analysed using the Kruskal–Wallis test, penalty analysis and correlation matrix.

The study revealed that saffron can interact with the perception of sour and bitter taste and has no significant effects on the sweetness. The colour and labelling generated expectations for quality and sweetness of the samples. When the disparity between the expectation and actual experience was occurred resulted in contrast/assimilation effects on the hedonic ratings and negatively impacted consumer acceptability of the product.

This study showed that the visual cues can modulate the expectation for particular sensory perceptions and also affect the hedonic experiences. Saffron adulteration can be identified by the consumers and can result in a significant decrease in the acceptability of the products. Hence, the practice of substituting saffron with ingredients with a similar colour in these products can be detrimental for business. Additionally, it was revealed that saffron colour is associated with the expected and actual sweet taste perception. Therefore, it is possible to manipulate yellow colour cues to reduce sweeteners in different food products that contain saffron.

The sensory characteristics and consumer perception of saffron have been rarely studied. This study revealed that flavour perception and quality determination of saffroned foods involves the combinations of different sensory modalities and cognitive (expectancy) inputs.