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This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.

In this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.

Applying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.

This paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.

The purpose of this paper is to investigate an alternative to established hysteresis models.

Different mathematical representations of the magnetic hysteresis are compared and some differences are briefly discussed. After this, the application of the T(x) function is presented and an inductor model is developed. Implementation details of the used transient circuit simulator code are further discussed. From real measurement results, parameters for the model are extracted. The results of the final simulation are finally discussed and compared to measurements.

The T(x) function possesses a fast mathematical formulation with very good accuracy. It is shown that this formulation is very well suited for an implementation in transient circuit simulator codes. Simulation results using the developed model are in very good agreement with measurements.

For the purpose of this paper, only soft magnetic materials were considered. However, literature suggests, that the T(x) function can be extended to hard magnetic materials. Investigations on this topic are considered as future work.

While the mathematical background of the T(x) function is very well presented in the referenced papers, the application in a model of a real device is not very well discussed yet. The presented paper is directly applicable to typical problems in the field of power electronics.

This study explored use of big data analytics (BDA) to analyse data of a large number of construction firms to develop a construction business failure prediction model (CB-FPM). Careful analysis of literature revealed financial ratios as the best form of variable for this problem. Because of MapReduce’s unsuitability for iteration problems involved in developing CB-FPMs, various BDA initiatives for iteration problems were identified. A BDA framework for developing CB-FPM was proposed. It was validated by using 150,000 datacells of 30,000 construction firms, artificial neural network, Amazon Elastic Compute Cloud, Apache Spark and the R software. The BDA CB-FPM was developed in eight seconds while the same process without BDA was aborted after nine hours without success. This shows the issue of not wanting to use large dataset to develop CB-FPM due to tedious duration is resolvable by applying BDA technique. The BDA CB-FPM largely outperformed an ordinary CB-FPM developed with a dataset of 200 construction firms, proving that use of larger sample size with the aid of BDA, leads to better performing CB-FPMs. The high financial and social cost associated with misclassifications (i.e. model error) thus makes adoption of BDA CB-FPMs very important for, among others, financiers, clients and policy makers.