报告题目：Resolving families of operators and subordination principles for equations with fractional derivatives

主 讲 人：Vladimir E. Fedorov (Chelyabinsk State University, Russia)

报告邀请人：李树光 副教授

报 告 时间：2026年11月06日上午08:30-11:30

报告地点：数理楼 224

报告摘要：As is well known, initial value problems for differential equations in Banach spaces represent an abstract form of initial-boundary value problems for partial differential equations and systems of them. When studying such equations, an important issue is the existence of a resolving family of operators for the equation, which is equivalent to the issue of the well-posedness of the initial problem for it. Equations with fractional derivatives of Dzhrbashyan-Nersesyan are considered; special cases of them include fractional derivatives of Gerasimov-Caputo, Riemann–Liouville, and Hilfer. Theorems on the generation of analytic and strongly continuous resolving families of operators for such equations are proved. It is shown that belonging to the class of generating operators depends on two out of n+1 parameters of the Dzhrbashyan-Nersesyan derivative - on the first parameter and on the sum of all parameters minus one, i.e., on the order of the derivative. The principles of subordination for these two parameters of equations with such derivatives have been proven. Solvability issues for corresponding linear inhomogeneous equations have been studied. The obtained results have been used in the study of initial-boundary value problems for equations of mathematical physics of fractional order with respect to time.od.

个人简历：Fedorov Vladimir Evgenevich教授是俄罗斯数学领域的知名专家，曾任车里雅宾斯克国立大学学术副校长，现任车里雅宾斯克国立大学数学分析系主任、教授、物理数学科学博士，长期致力于微分方程、动力系统与最优控制领域的科研与教学工作，在俄罗斯及国际数学领域具备广泛的学术影响力。先后荣获国际ISAAC青年科学家奖、车里雅宾斯克国立大学荣誉教授、沙德林斯克国立师范大学荣誉教授、俄罗斯联邦教育工作荣誉工作者称号等荣誉；累计发表高水平学术论文200余篇，研究成果被国内外同行广泛引用。担任Computational Mathematics and Modeling等多个学术期刊的主编和编委。