AAM Seminar - Strongly continuous - analytic resolving families of operators for fractional diff eqn

Strongly continuous and analytic resolving families of operators for fractional differential equations in Banach spaces
Prof. Dr. Vladimir E. Fedorov
Chelyabinsk State University, Russia

Abstract:
Conditions for a linear closed operator in a Banach space are obtained that are necessary and sufficient to generate a resolving family of operators for a fractional differential equation. The cases of fractional derivatives of Riemann-Liouville, Hilfer, Dzhrbashyan-Nersesyan are considered. These results are generalizations of the Hille-Yosida theorem for resolving semigroups of first-order equations. Similar theorems have been proved for analytic in a sector resolving families of operators. The results are used in the research of initial value problems for linear and quasilinear equations in Banach spaces. Abstract results are applied to the study of various initial boundary value problems for partial differential equations and their systems.

Biography:
Vladimir E. Fedorov graduated from Chelyabinsk State University in 1994. He obtained the degree of Doctor of Physical and Mathematical Sciences in 2005. He is currently a full Professor and the Head of the Department of Mathematical Analysis at the Faculty of Mathematics, Chelyabinsk State University, Russia. Prof. V.E. Fedorov has more than 160 scientific publications indexed in the Scopus database. Under his scientific supervision, 15 dissertations for the degree of Сandidate of Physical and Mathematical Sciences (Ph.D.) and several dozen Master's theses were defended. Prof. V. E. Fedorov is the Editor-in-Chief of the journal
of Computational Mathematics and Modeling, the Deputy Editor-in-Chief of Chelyabinsk Physical and Mathematical Journal, and the member of the Editorial Boards of several international mathematical journals. His current research interests include Fractional Differential Equations.