Strict LpSolutions for Nonautonomous Fractional Evolution Equations

MSC 2010: 26A33, 34A08, 34K3

Fractional evolution equations in Banach spaces

IV+107hlm.;24c

Perturbation and approximation properties for abstract evolution equations of fractional order

We investigate the abstract evolution equation of fractional order Dau = au, a > 0, where Da is the Caputo fractional derivative of order a and A is an unbounded closed operator in a Banach space X. Some perturbation properties are presented, generalizing known facts about Co-semigroups and cosine operator functions

An Analysis of the Rayleigh-Stokes problem for a Generalized Second-Grade Fluid

We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data $v$, including $v\in L^2(\Omega)$. A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.Comment: 23 pp, 4 figures. The error analysis of the fully discrete scheme is shortene

An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, contract No DO1–205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria

Принцип за субординация на обобщени дробни еволюционни уравнения

ИМИ-БАН, 15.11.2022 г., присъждане на научна степен "доктор на науките" на Емилия Григорова Бажлекова. [Bazhlekova Emilia Grigorova; Бажлекова Емилия Григорова