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The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.

The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.

A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.

The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters.

The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations.

It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow.

This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

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.

Hydro-viscous drive (HVD) clutches are widely used in equipment requiring soft start, such as fans and pumps, to transmit torque and adjust speed by changing the gap distance between friction pairs. This paper aims to propose a novel two-parameter evaluation method for HVD during the mixed lubrication stage. The objective is to develop an effective model that establishes the relationship between these parameters and the actual surface topography.

In the presented methods, the fractal features of the real manufacturing surface are calculated based on the power spectrum function by the ultra-depth three-dimensional microscope. After that, the hybrid friction model of the friction plate is established based on mixed elasto-hydrodynamic lubrication theory, boundary friction model and fractal theory. Then the torque and load bearing characteristics of the clutch are obtained, and the influences of the surface fractal features are investigated and discussed. Finally, the Weierstrass–Mandelbrot function is adopted for the surface topography characterization and evaluation.

The results indicate that the proposed method exhibits good accuracy, while the speed difference between the friction pair exceeds 2,500 rpm. It is concluded that this paper proposed a way to evaluate the torque and loading capacity of HVD considering the real manufacturing surface topography and is helpful for surface optimization.

The originality and value of this study lie in its development of a novel torque and load bearing capacity evaluation method for HVD in mixed lubrication stage, considering manufacturing surface topography and describing the real manufacturing surface.

Advanced big data analysis and machine learning methods are concurrently used to unleash the value of the data generated by government hotline and help devise intelligent applications including automated process management, standard construction and more accurate dispatched orders to build high-quality government service platforms as more widely data-driven methods are in the process.

In this study, based on the influence of the record specifications of texts related to work orders generated by the government hotline, machine learning tools are implemented and compared to optimize classify dispatching tasks by performing exploratory studies on the hotline work order text, including linguistics analysis of text feature processing, new word discovery, text clustering and text classification.

The complexity of the content of the work order is reduced by applying more standardized writing specifications based on combining text grammar numerical features. So, order dispatch success prediction accuracy rate reaches 89.6 per cent after running the LSTM model.

The proposed method can help improve the current dispatching processes run by the government hotline, better guide staff to standardize the writing format of work orders, improve the accuracy of order dispatching and provide innovative support to the current mechanism.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

This study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.

The parabolic AD equations are reduced to the nonhomogeneous elliptic system of partial differential equations by utilizing the Chebyshev spectral collocation method (ChSCM) in the temporal variable. The implicit-explicit local differential transform method (IELDTM) is constructed over two- and three-dimensional meshes using continuity equations of the neighbor representations with either explicit or implicit forms in related directions. The IELDTM yields an overdetermined or underdetermined system of algebraic equations solved in the least square sense.

The IELDTM has proven to have excellent convergence properties by experimentally illustrating both h-refinement and p-refinement outcomes. A distinctive feature of the IELDTM over the existing numerical techniques is optimizing the local spatial degrees of freedom. It has been proven that the IELDTM provides more accurate results with far fewer degrees of freedom than the finite difference, finite element and spectral methods.

This study shows the derivation, applicability and performance of the IELDTM for solving 2D and 3D advection-diffusion equations. It has been demonstrated that the IELDTM can be a competitive numerical method for addressing high-space dimensional-parabolic partial differential equations (PDEs) arising in various fields of science and engineering. The novel ChSCM-IELDTM hybridization has been proven to have distinct advantages, such as continuous utilization of time integration and optimized formulation of spatial approximations. Furthermore, the novel ChSCM-IELDTM hybridization can be adapted to address various other types of PDEs by modifying the theoretical derivation accordingly.

This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.

Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators. Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration. This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration, including a brief introduction of short-pitch irregularities, associated high frequency vibration in railway bogie, typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.

The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms. The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components. The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure, and the fatigue crack usually initiates from the defect of the weld seam. Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities. The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment, and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.

The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.

In this study, supervision and control of the possible problems among people over a large area with a limited number of drone cameras and security staff is established.

These drones, namely unmanned aerial vehicles (UAVs) will be adaptively and automatically distributed over the crowds to control and track the communities by the proposed system. Since crowds are mobile, the design of the drone clusters will be simultaneously re-organized according to densities and distributions of people. An adaptive and dynamic distribution and routing mechanism of UAV fleets for crowds is implemented to control a specific given region. The nine popular clustering algorithms have been used and tested in the presented mechanism to gain better performance.

The nine popular clustering algorithms have been used and tested in the presented mechanism to gain better performance. An outperformed clustering performance from the aggregated model has been received when compared with a singular clustering method over five different test cases about crowds of human distributions. This study has three basic components. The first one is to divide the human crowds into clusters. The second one is to determine an optimum route of UAVs over clusters. The last one is to direct the most appropriate security personnel to the events that occurred.

This study has three basic components. The first one is to divide the human crowds into clusters. The second one is to determine an optimum route of UAVs over clusters. The last one is to direct the most appropriate security personnel to the events that occurred.

The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction.

The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem.

The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes.

All results are presented graphically and all physical quantities are computed and tabulated.