Fundamental scientific research is conducted in the following areas:

• Numerical methods for solving differential equations of fractional order;
• Mathematical modeling of geophysical and particle physics processes;
• Fractional calculus and differential equations of fractional and distributed order;
• Development and implementation of mathematical models of thermophysical and physical-chemical properties of nanosystems;
• Development of theory, methods, and algorithms for robust machine learning and multilayer neural-like systems based on the theory of aggregating functions and operations;
• Management of network and non-local systems with distributed parameters;
• Boundary value problems for mixed-type equations and their application to modeling dynamic systems;
• Research of interaction mechanisms between economic agents in markets with uncertain characteristics of goods;
• Research of the features of electromagnetic radiation transmission in periodic micro- and nanocapillary structures;
• Self-organizing cognitive multi-agent control intelligent systems for synthesizing purposeful behavior of a team of autonomous robots in intelligent habitats;
• Development of methods and algorithms for decision-making and control in heterophase intelligent systems based on multi-agent self-organization;
• Development of methods for studying the impact of global natural factors on regional socio-economic systems in order to reduce the risks associated with them;
• Development, implementation, and research of algorithms for assessing information security based on modern analysis methods;
• Mechanisms for managing the advanced development of a region, taking into account the influence of the knowledge economy and intelligent habitat systems;
• Development of methods for speech recognition in complex acoustic scenes based on multi-agent recursive cognitive architectures;
• Development of methods for creating software systems for virtual prototyping of engineering network systems.
• Development of methods and tools for designing and virtual prototyping of bionano devices and systems of bionanorobotics using intelligent information and control systems;
• The North Caucasus and the world of the peoples of Eurasia: traditional and new forms of cultural interaction;
• Political anthropology and socio-political history of the peoples of the Central and North-Western Caucasus in the 16th – early 20th centuries;
• Traditional genres of Adyghe and Karachay-Balkar folklore: systematization, textology, and research;
• Modern Literatures and Literature of the Diaspora of the Adyghe (Kabardian, Circassian, Adygei) and Karachay-Balkar peoples: Features of the Literary Process, Chronicle, and Creative Individualities;
• Kabardian-Circassian and Karachay-Balkar Languages: Systemic Relations in Grammar and Lexicon; Functioning;
• Kabardino-Balkaria in the Context of Historical and Cultural Dynamics in the 20th and Early 21st Centuries;
• Historical Consciousness and Historical Science in the North Caucasus: Problems of Interaction in the Modern Socio-Cultural Context (Based on the Kabardino-Balkarian Republic);
• Construction based on geoinformation methodology of numerical-cartographic integral complex assessments of natural hazards of selected geosystems of the northern slope of the Greater Caucasus;
• Research of the dynamics of the composition of natural waters of the North Caucasus depending on the altitude zonality and bioindication of the influence of high-altitude conditions on living organisms;
• Research of additive technology of prototyping parts of robotic devices based on modeling in physically correct virtual environments;
• The main problems of the development of the socio-political situation in Kabardino-Balkaria at the end of the 20th century and the beginning of the 21st century;
• Research of the socio-ecosystemic consequences of the robotization of the agricultural sector in the North Caucasus region;
• Creation and selection of new genotypes of grain crops with high productivity and grain quality, resistance to bio- and abio-environmental factors, and production of seeds of higher reproductions of new varieties and hybrids;
• Improvement of the integrated protection system for varieties and hybrids of field crops;
• Establishment on the basis of the database of the effectiveness of the application of fertilizer systems, methods of sustainable production of plant products of the specified quantity, quality and preservation of the fertility of the ordinary chernozem
  carbonate in specific agro-landscape conditions of the Central Ciscaucasia;
• Allocation of new potato genotypes with high productivity and quality of tubers, resistance to bio- and abio-environmental factors and production of seed material of potatoes, improved on the basis of in vitro;
• Improvement of the technology of cultivating new varieties and hybrids of main field crops in the steppe and mountain zones of the Kabardino-Balkarian Republic;
• Development of a methodology for managing the selection process of forming desirable genotypes of farm animals for different technologies of keeping, taking into account the physiological need for nutrients;
• Improvement of methods of breeding and selection work with the Kabardino breed of horses in order to use it rationally and increase its genetic potential.