Systems of Fractional Partial Differential Equations

• 主讲人：Murat O. Mamchuev (Institute of Applied Mathematics and Automation, KBSC RAS)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-03-30 21:00 - 2023-03-30 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/FE999300C34E3C58E76EAA978AC3313F
Valid Until: 2027-04-30 23:59

 

Abstract: In recent years, considerable interest in differential equations of fractional order has been caused by their numerous applications in many fields of science and technology. This circumstance served as an impetus for the development of the theory of boundary value problems for equations and systems of partial differential equations of fractional order, which has now become one of the intensively developing areas of modern mathematics.

We describe classes of well-posed initial and initial-boundary value problems for linear systems of partial differential equations of fractional order not exceeding one. We will show that these systems can be divided into two different types, which differ significantly in terms of setting correct boundary value problems. The first type includes systems with sign-definite eigenvalues of matrix coefficients in the main part. The second type includes systems of matrix coefficients in the main part of which have eigenvalues of different signs.

 

Bio: Murat O. Mamchuev graduated from Karachay-Cherkess State University in 1998. In 2005, he received the Candidate of Science degree at Kazan State University named after V.I. Ulyanov-Lenin (currently Kazan Federal University). And in 2021 he received the Doctor of Sciences degree at Lomonosov Moscow State University. He is now Head of the Department of Fractional Calculus at the Institute of Applied Mathematics and Automation of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences. Since 2022, he is a Professor at the Department of Computer Technologies and Information Security of Kabardino-Balkarian State University. Author of more than 100 scientific papers. His research interests include fractional calculus, fractional order differential equations and systems of such equations, methods for analyzing the correctness of statements and solvability of initial and boundary value problems, and mathematical models based on fractional order differential equations. In 2008-2009, M. Mamchuev became the Laureate of the grant in the field of natural and human sciences "Candidates of Sciences of Russian Academy of Sciences" of the Foundation for the Promotion of National Science. Since 2014, he is an Expert in the scientific and technical sphere of the Ministry of Education and Science of the Russian Federation.