The scientific conclusions obtained by the group of the teaching staff of the Azerbaijan University, by the decision of the Presidium of ANAS, were included in the report of the Department of Physics, Mathematics and Technical Sciences on the most important results of research carried out in 2020. Success achieved by a team of scientists in the person of the Vice-Rector for Science of the University, Doctor of Mathematical Sciences Yusif Gasimov, Head of the Science Department, Doctor of Philosophy in Mathematics Latifa Agamalyeva, Professor of the Department of Mathematics and Informatics, Doctor of Mathematical Sciences Agil Khanmammadov, lecturers of the department - Doctor of Philosophy in Mathematics Bahram Azizov, Asif Pashayev and Nigar Gafarova, is for the first time in the history of the Azerbaijan University a logical continuation of purposeful and consistent work to increase the scientific prestige of the university. This success is also important from the point of view of the fact that the report includes the scientific findings of a total of 6 institutions that are not part of the structure of ANAS, as well as participation in the report of the Azerbaijan University as the only private university. In connection with the results of the research, 8 articles were published in journals with an impact factor.

The topic of the research work included in the scientific report of the institution coordinating scientific activities in Azerbaijan: "Development of methods for solving some inverse and direct problems for differential and integral equations, expert systems, decision-making algorithms in a fuzzy statement and their practical application."

Summary of scientific findings

In the research work, methods were developed for solving some inverse and direct problems for differential and integral equations. In addition, expert systems, algorithms for making decisions in a fuzzy statement were proposed, and a simulation was performed for their specific practical tasks. At the same time, for a more adequate description of physical processes, models of fractional differential equations were used and effective methods were developed for the numerical solution of these models.

List of published scientific articles on the topic

1. Can, N.H., Nikan, O., Rasoulizadeh, M.N., Jafari, H., & Gasimov, Y.S. (2020). Numerical computation of the time non-linear fractional generalized equal width model arising in shallow water channel. Thermal Science, 24(Suppl. 1), 49-58 (Web of Science Impact Factor - 1.574).

2. Y.S. Gasimov, Sh.E. Guseynov, J.E. Napoles-Valdes. On some properties of limit cycles of the Biryukov equation. Proceedings of the Institute of Mathematics and Mechanics, Vol.46, No2, 2020. (Web of Science Emerging Source Citation Index).

3. Pourghanbar S., Manafian J., Ranjbar M., Aliyeva A., GasimovY.S. An efficient alternating direction explicit method for solving a nonlinear partial differential equation. Mathematical Problems in Engineering, Vol.2020, Article ID 9647416, 12 pages.

4. Khanmamedov, A. Kh. O., & Makhmudova, M. G. K. (2020). On the inverse dispersion problem for the Schredinger equation with an additional linear potential. Theoretical and Mathematical Physics, 202 (1), 66-80 (Web of Science Impact Factor - 0.901).

5. Khanmamedov, A. Kh. O., & Makhmudova, M. G. K. (2020). About transformation operator for the Schredinger equation with additional linear potential. Functional Analysis and Its Applications, 54 (1), 93-96) (Web of Science Impact Factor - 0.712).

6. Latifova, A. R., & Khanmamedov, A. K. (2020). Inverse spectral problem for the one-dimensional Shtark operator on the semiaxis. Ukrains' kyi Matematychnyi Zhurnal, 72 (4), 494-50 (Web of Science Impact Factor - 0.326).

7. Bagirova, S. M., & Khanmamedov, A. Kh. (2020). On the zeros of the modified Bessel function of the second kind. In Complex Analysis, Mathematical Physics and Nonlinear Equations (pp. 15-16) (Web of Science Impact Factor - 0.774).

8. Khanmamedov, A. K., & Gafarova, N. F. (2020). Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition. Journal of Inverse and Ill-posed Problems, 1 (Web of Science Impact Factor – 0.926).

9. Bakhram Azizov, Asif Pashayev, Yusif Gasimov. "Soft computing" technologies of hybrid model structure for the automated control of flights. International conference on Natural Sciences & Technologies-ICONAT-2020, 20-22 August, 2020.

10. Yusif Gasimov, Asif Pashayev, Bakhram Azizov. Modelling of Fuzzy Logic Toolbox is FIS- a structure is the system of unclear conclusion (Fuzzy

Inference System) using the MATLAB program. International conference on Natural Sciences & Technologies-ICONAT-2020, 20-22 August, 2020.

Public Relations Department
23.02.2021