The scientific substantiations of quality have been applied to models that pertain to mathematical statistics, the probability theory, the information theory, fuzzy systems, graphic methods, time series, and algebraic and numerical methods. To these, this article aims to present a new method of applying mathematical modelling in an economy based on knowledge, by using the concept of the definite integral, the composite function, and mathematical optimisation. The research methods used in the realisation of this article are bibliographic research, creation of new models, and problem-solving. Mathematical modelling, the simulation of the quality of life, etc. are methods and techniques of both theoretical and practical scientific approach, which are likely to lead to a better understanding of the role of quality in this field, as well as leading to the sustainable development of quality by providing new practical solutions to achieve a quality, always superior to the one obtained previously. In this article, the author presents some personal contributions to the scientific approach to quality, through modelling and simulation of the quality of life, and management of the quality of life in an economy based on knowledge.

The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

The aim of this paper is to highlight the influence of economic and qualitative factors on steel production globally, as well in the EU, US, and China, using a dataset corresponding to the period 2000–2015. The research methods used are the study of specialist literature, problematisation, modelling, and simulation using Statistical Package for the Social Sciences (SPSS) software. The main conclusion of this paper is that, on long term, the steel production is largely influenced by the rate of real economic growth and by car production, even if in the short term the correlation is not obvious. Likewise, qualitative factors affect the steel industry in the context of current regulations on reducing carbon emissions and ensuring sustainable development. An additional aim of the present study is to define entropy in the sustainable development of steel production, as well as illustrate some of its properties and the quality management modelling of the research process in steel production.

New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model’s Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation.