Modern problems of mathematical physics
December 3, 2025, 14:00. A joint seminar of the Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan and the Institute of Applied Mathematics and Automation KBSC RAS and Analysis & PDE Center of Ghent University (Belgium) on Modern Problems of Mathematical Physics.
Speaker: Professor Batirkhan Turmetov, Khoja Akhmet Yasawi International Turkish-Kazakh University.
Topic of the report: The Method of Normalized Systems of Functions and Its Application to Constructing Solutions of Fractional-Order Differential Equations.
Abstract: This report presents information about a method for constructing solutions of fractional-order differential equations. This method, called the method of normalized systems, was developed in the work of B.A. Bondarenko [1] and later modified in the works of V.V. Karachik [2,3]. In those studies, solutions of various integer-order differential equations were constructed. In the present work, the method of normalized systems is applied to constructing solutions of fractional-order differential equations. Various classes of fractional-order differential equations are considered. Explicit solutions of homogeneous and nonhomogeneous fractional-order equations are constructed. New classes of special functions are obtained, and their properties are studied.
1.Bondarenko B.A. Operator Algorithms in Differential Equations. Tashkent: Fan, 1984.
2.Karachik V.V., Normalized System of Functions with Respect to the Laplace Operator and Its Applications, Journal of Mathematical Analysis and Applications, 287, No. 2 (2003), 577–592.
3.Karachik V.V., The Method of Normalized Systems of Functions. Chelyabinsk: Publishing Center of SUSU, 2014. – 452 p.
Join the Zoom conference:
https://us06web.zoom.us/j/88273567781?pwd=6TMH3UOjALVQmLsLlm6vTMPo5YpCYr.1
Conference ID: 882 7356 7781
Access code: 151325
Seminar leaders: Sh. A. Alimov, academician, A. V. Pskhu, professor, R. R. Ashurov, professor.
Seminar secretary: R. T. Zunnunov.