Speaker: Vladimir E. Fedorov, Head of Mathematical Analysis Department, Chelyabinsk State University

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom link : A link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  fractional differential equation, Cauchy type problem, resolving family of operators, Hille--Yosida type conditions, analytic resolving family, Hilfer fractional derivative, initial boundary value problem

Abstract: The issues of unique solvability of initial problems for equations solved with respect to a fractional derivative are investigated. As an example, the Cauchy type problem for a differential equation with the Hilfer fractional derivative  in a Banach space is considered. Necessary and sufficient conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation are obtained in terms of the resolvent of a linear closed operator at an unknown function in equation \cite{F1}. These conditions are a generalization of the Hille--Yosida conditions for the case of fractional order equations. A theorem on necessary and sufficient conditions for the existence of an analytical resolving family of the fractional differential equation is also proved \cite{F2}. Under such conditions, the solvability of linear inhomogeneous equations and some classes of quasi-linear equations is investigated \cite{F3}. Similar results were obtained for fractional differential equations with the Dzhrbashyan–Nersesyan derivative \cite{F4}, for multi-term differential equations with Riemann–Liouville \cite{F5} or Gerasimov–Caputo derivatives \cite{F6}, for equations with distributed fractional derivatives \cite{F7,F8,F9}. Abstract results are used in the study of initial boundary value problems for partial differential equations.

Biography: Vladimir Evgenievich Fedorov. Born on March 01, 1972. Head of the Department of Mathematical Analysis, Faculty of Mathematics, Chelyabinsk State University. Education: Chelyabinsk State University, 1994. Doctor of Physical and Mathematical Sciences (since 2005), Professor (since 2007).

Honorary Professor of Chelyabinsk State University, Honorary Professor of Shadrinsk State Pedagogical University, Honorary Worker of Education of the Russian Federation. Winner of the Prize for Young Scientists of the International Society for Analysis, Its Applications and Computations (ISAAC Award for Young Scientists, 2011) – "for achievements in semigroup theory and control theory".

Editor-in-Chief of Computational Mathematics and Modeling, Deputy Editor-in-Chief of the Chelyabinsk Physical and Mathematical Journal, member of the Editorial Board of the journals: Bulletin of Irkutsk State University. Series Mathematics; Progress in Fractional Differentiation and Applications; International Journal of Mathematical Modelling and Numerical Optimisation.

Bibliography

[1] Vladimir E. Fedorov, Wei-Shih Du, Marko Kosti´c, Marina V. Plekhanova, Anton S. Skorynin. “Criterion of the existence of a strongly continuous resolving family for a fractional differential equation with the Hilfer derivative”. In: Fractal and Fractional 9.2 (2025), p. 81.
[2] Vladimir Fedorov, Yusupjon Apakov, Anton Skorynin. “Analytic resolving families of operators for linear equations with Hilfer derivative”. In: Journal of Mathematical Sciences 277.3 (2023), pp. 385–402.
[3] Vladimir E. Fedorov, Anton S. Skorynin. “A class of quasilinear equations with Hilfer derivatives”. In: Mathematical Notes 115.5 (2024), pp. 817–828.
[4] Vladimir E. Fedorov, Marina V. Plekhanova, Elizaveta M. Izhberdeeva. “Analytic resolving families for equations with the Dzhrbashyan — Nersesyan fractional derivative”. In: Fractal and Fractional 6.10 (2022), p. 541.
[5] Vladimir E. Fedorov, Mikhail M. Turov. “Multi-term equations with Riemann—Liouville derivatives and Holder type function spaces”. In: Boletin de la Sociedad Matematica Mexicana 29 (2023), p.42.
[6] Vladimir E. Fedorov, Kseniya V. Boyko. “Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case”. In: Mathematics 10.24 (2022),p. 4699.
[7] Vladimir E. Fedorov, Nikolay V. Filin. “On strongly continuous resolving families of operators for fractional distributed order equations”. In: Fractal and Fractional 5.1 (2021), p. 20.
[8] Vladimir E. Fedorov, Nikolay V. Filin. “A class of quasilinear equations with distributed Gerasimov – Caputo derivatives”. In: Mathematics 11.11 (2023), p. 2472.
[9] Vladimir E. Fedorov, Aliya A. Abdrakhmanova. “Linear equations with distributed Riemann–Liouville derivatives given by Stieltjes integrals and their analytic resolving families of operators”. In: Lobachevskii Journal of Mathematics 44.8 (2023), pp. 3277–3291