The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

A geologic and geomorphologic study aimed at solving some geological and geotechnical problems, regarding the massive seepage of meteoric waters in the coastal cliffs of the Island of Procida (Naples Bay, Southern Italy) composed of both tuffs and loose pyroclastic deposits, has been carried out in the geosites of Terra Murata (Middle Ages village and coastal cliff towards the Corricella Bay) and Centane-Panoramica (coastal cliff facing on the Tyrrhenian Sea).

A detailed geologic and geomorphologic survey has allowed to suggest solutions to the applied geological and geotechnical problems related to the occurrence of massive seepages of waters at the physical interface between pyroclastic rocks and loose pyroclastic deposits, characterized by different density, permeability and porosity and also controlled by a dense network of fractures, involving the pyroclastic deposits cropping out in the selected areas.

Field sampling and geotechnical laboratory analyses have been carried out to calculate the values of main geotechnical parameters of the yellow tuffs cropping out at the Terra Murata Promontory. At the same time, a detailed monitoring of the seepages of waters has been carried out through a detailed geological survey of the tuff outcrops of the promontory. The obtained results have suggested a strong control from both the geomorphologic instability of the coastal cliff and tectonic setting. At the Centane-Panoramica geosite, the geological survey, coupled with geotechnical analyses and standard penetrometric tests, has accordingly evidenced that the geomorphologic instability was mainly concentrated in the sectors of the tuff coastal cliffs facing seawards towards the Tyrrhenian Sea.

This research paper explores the influence of first-order chemical reactions on the sustainable properties of electrically conducting magnetohydrodynamic (MHD) fluids in a vertical channel with the unique characteristics of Jeffrey fluid flow. The mathematical model of MHD flow with Jeffrey fluid and chemical reaction incorporates the impacts of viscous dissipation, Joule heating, and a non-Newtonian fluid model with viscoelastic properties in the flow regions. The governing equations of the flow field were solved using the finite difference method, and the impacts of flow parameters on the flow characteristics were discussed numerically using a graphical representation. It’s revealed that increasing the Jeffrey parameter results in a decline in the velocity field profiles. Also, species concentration field profiles decline with higher values of the destruction chemical reaction parameter. The findings of this study have significant implications for various engineering applications, including energy generation, aerospace engineering, and material processing. Additionally, the inclusion of Jeffrey’s fluid flow introduces a viscoelastic component, enhancing the complexity of the fluid dynamics.

In our study, we examined 11 designated tourist destinations in Hungary, which can also be interpreted as tourism products including services, infrastructure and attractions. The National Tourism Development Strategy (NTS) also puts a strong emphasis on digitalisation, as it is an unstoppable process with a significant impact on tourism, thanks to globalisation, increasing competition, accelerating information flows and the dominant paradigm shifts on the demand and supply side. We used both qualitative and quantitative methods in our primary research. First, we conducted in-depth interviews with several important tourism service providers in Hungary on the topic of the digitalisation of tourism. A professional questionnaire, addressed to the offices responsible for destination management was distributed in the designated tourist destinations in Hungary in order to get a more comprehensive picture of the attitudes towards digitalisation in the regions under study. In the course of our work, we managed to classify the destinations into three distinctly different clusters. Our hypothesis—that the higher the digitalisation of a tourist destination is, the higher the average length of stay—was partially confirmed by calculating the regional value of the digitalisation, logistic regression analysis, slope and the individual factor categories.