In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

The most important goals on the Europe 2020 Strategy contained were the climate/energy goals, which determine the achievement of other targets of the strategy. The aim of the article is to evaluate the implementation of the climate/energy targets of the Europe 2020 Strategy by the EU Member States in 2010 and 2019 and to compare the results achieved by them. To measure them, a basic set of indicators was used for this purpose, which the authors supplemented with additional indicators. The evaluation was done using the taxonomic and zero-unitarization method. They made it possible to integrate all indicators. Moreover, the added value in relation to other studies is: the use of individual indicators, instead of general ones obtaining additional information about the internal structure and nature of the implementation of multidimensional groups of targets and focusing solely on the achievement of climate/energy targets. The achieved results not only reflect the progress of the Member States in achieving the climate/energy targets and the differences in the level of achieving objectives between countries, but they are also discussion on future strategic objectives, their indicators and necessary directions for a further community climate/energy policy.

The purpose of the article is to analyse the level of energy poverty in the EU member states for the period 2010–2020. The research was carried out on the basis of the author’s Synthetic Multidimensional Energy Poverty Index created on the basis of the zero-unitarization method. The proposed index allowed for the integration of 4 out of 13 indicators provided for the study of energy poverty in the Recommendation of the European Commission 2020, and 1 selected by the authors. The assessment of changes in the level of energy poverty over time in 24 EU countries using the method used adds value compared to the assessment methods used so far in this area. Previous studies of energy poverty levels have focused on individual countries or small groups of countries. Rarely have such studies covered the majority of EU countries, and even more rarely have they been conducted over a long period of time. The study carried out showed significant differences in energy poverty levels among EU members. Results obtained not only reflect the progress of member countries in reducing energy poverty, but also allow for a discussion on future approaches regarding its reduction.

In this paper, we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important centre manifolds, and study their bifurcation. Saddle-node and period-doubling bifurcation route to chaos are exhibited via numerical simulations.

Research and development (R&D) spending in the energy sector, which is aimed at exploring ways to reduce greenhouse gas emissions, among other things, plays a vital role in achieving the goal of climate neutrality. The purpose of this paper is to assess the environmental performance of R&D spending in the energy sector of selected EU member states from 2011–2017/2019, and to compare the results. Taxonomic research with the zero unitarization method was used, which enabled a synthetic assessment of EU countries according to the environmental performance of the total spending in the energy sector and an analysis of the changes in performance for six categories of spending in this area. The assessment of changes in the environmental performance of individual categories of R&D spending over time using the applied method was an added value compared with the assessment methods previously used in this area. The study found that there were significant differences in the level of environmental efficiency of R&D expenditures in the energy sector between countries, changes in environmental efficiency in most of the countries studied were not satisfactory, the most environmentally efficient expenditures were on renewable energy, other power and storage, hydro and fuel cell technologies, and the least on fossil fuels and nuclear energy. The results reflected both the member states’ progress towards climate neutrality and the discussion on the environmental performance of the means and directions of actions aimed at this.