IRN AP14972818 “Development of methods for constructing fundamental solutions of non-classical equations of high-order mathematical physics”.

The relevance of the project. The progress of modern science has shown that non-classical equations are a good model of real physical, chemical and biological processes, and this has determined the relevance of this project. Until recently, boundary value problems for second-order differential equations were studied to a greater extent, but research suggests that equations of the third and higher orders play an equally important role in the study of physical processes and phenomena of the real world. No less relevant are the problems associated with the consideration of differential equations of the fourth order. The need to study fourth-order equations is due to their application in physical problems, for example, plate bending theory, shell theory and use in electronics and optoelectronics devices, etc. The novelty of the project is the research and construction of solutions to unexplored problems for various non-classical equations of high-order mathematical physics using fundamental solutions. Solutions to the problems under consideration, as a rule, will be presented through special functions, the properties of which are planned to be studied during the implementation of the project.

The purpose of the project. The aim of the project is to develop methods for constructing fundamental solutions of non-classical equations of high-order mathematical physics. Determination of solvability conditions for boundary value problems and direct solution of boundary value problems for high-order partial differential equations using the obtained fundamental solutions.

Expected results:

1. Fundamental solutions for unexplored non-classical equations of high-order mathematical physics will be constructed and their features will be investigated;
2. The unambiguous solvability of a number of boundary value problems for the equations under consideration on both infinite and finite domains will be investigated using the Green’s function method;
3. New formulas of decomposition, integral representations and analytical continuation of hypergeometric functions of many variables will be obtained.

Composition of the research group:
1. Ryskan Aynur Ryskankyzy, Doctor of Philosophy, art.Rev., gylym zhetekshi zhane zhobany oryndaushy.Scopus H-index: 2, ORCID / 0000-0002-8764-4751, Scopus Author ID: 57209534432.
2. Berdyshev Abdumauvlen Suleymanovich, PhD, Professor, scientific consultant. H-index in Scopus: 10, h-Index in WoS: 8,ORCHID: 0000-0002-1228-8246, Scopus author ID: 8916505200.