@article{Zharullayev_Kanguzhin_Konyrkulzhayeva_2019, title={Green’s function of differential operators on a star-shaped graph with common boundary conditions}, volume={101}, url={https://bm.kaznu.kz/index.php/kaznu/article/view/601}, DOI={10.26577/JMMCS-2019-1-601}, abstractNote={<p>Differential equations on graphs are one of the new sections of the theory of differential equations<br>and their fundamental concepts when analyzing models of a wide variety of problems in natural<br>science. It also arises when analyzing processes in complex systems, allowing as a set of onedimensional<br>continuum that interact only through the ends. The differential operator on graphs<br>is currently actively studying by mathematics and is found in many different applications, for<br>example, chemical kinetics, chemical technology, quantum mechanics, nanotechnology, biology,<br>organic chemistry, Markov processes, etc. In this paper, we construct the Green function of a<br>differential operator on a star shaped graph with common boundary conditions. In this paper, a<br>star shaped graph is a tree with one internal vertex and m leaves. Standard Kirchhoff conditions<br>are used at the interior vertices and mixed conditions at the boundary vertices. The edges of the<br>graph is a one-dimensional smooth regular manifold (curve). The top of the graph is a point.<br>The applicability of the results of this study is high both in theoretical terms - the development of<br>research in the theory of differential equations with memory on graphs, and in terms of applications<br>to biological processes, in particular neurobiology, nanotechnology, in the chemical and petroleum<br>industries.</p>}, number={1}, journal={Journal of Mathematics, Mechanics and Computer Science}, author={Zharullayev, D. B. and Kanguzhin, B. E. and Konyrkulzhayeva, M. N.}, year={2019}, month={Apr.}, pages={48–58} }