Marko Kostić

-Regularized -Resolvent Families: Regularity and Local Properties

We introduce the class of (local) -regularized -resolvent families and discuss its basic structural properties. In particular, our analysis covers subjects like regularity, perturbations, duality, spectral properties and subordination principles. We apply our results in the study of the backwards fractional diffusion-wave equation and provide several illustrative examples of differentiable -regularized -resolvent families.

On a class of time-fractional differential equations

AbstractIn this paper we investigate Cauchy problem for a class of time-fractional differential equation (0.1)

Perturbation Theory for Abstract Volterra Equations

\begin{gathered} D_t^\alpha u(t) + c_1 D_t^{\beta _1 } u(t) + \cdots + c_d D_t^{\beta _d } u(t) = Au(t), t > 0, \hfill \\ u^{(j)} (0) = x_j , j = 0, \cdots ,m - 1, \hfill \\ \end{gathered}

Degenerate k-regularized (C1, C2)-existence and uniqueness families

where A is a closed densely defined linear operator in a Banach space X, α > β1 > ... > βd > 0, cj are constants and m = ⌈α⌊. A new type of resolvent family corresponding to well-posedness of (0.1) is introduced. We derive the generation theorems, algebraic equations and approximation theorems for such resolvent families. Moreover, we give the exact solution for a kind of generalized fractional telegraph equations. Some examples are given as illustrations.

C-distribution semigroups and C-ultradistribution semigroups in locally convex spaces

We contribute to the existence theory of abstract time-fractional equations by stating the sufficient conditions for generation of not exponentially bounded α-times C-regularized resolvent families (α > 1) in sequentially complete locally convex spaces. We also consider the growth order of constructed solutions.

Application of an original soil tillage resistance sensor in spatial prediction of selected soil properties

We consider additive perturbation theorems for subgenerators of (a, k)-regularized C-resolvent families. A major part of our research is devoted to the study of perturbation properties of abstract time-fractional equations, primarily from their importance in modeling of various physical phenomena. We illustrate the results with several examples.

Structural theorems for ultradistribution semigroups

This paper is devoted to the study of abstract time-fractional equations of the following form: , , , , where , and are closed linear operators on a sequentially complete locally convex space , , is an -valued function, and denotes the Caputo fractional derivative of order (Bazhlekova (2001)). We introduce and systematically analyze various classes of -regularized ()-existence and uniqueness (propagation) families, continuing in such a way the researches raised in (de Laubenfels (1999, 1991), Kostic (Preprint), and Xiao and Liang (2003, 2002). The obtained results are illustrated with several examples.

Abstract Volterra Integro-Differential Equations: Approximation and Convergence of Resolvent Operator Families

En este articulo, consideramos varias clases de familias k-regularizadas (C1, C2)-de existencia y unicidad. El principal objetivo de este trabajo es mostrar como las tecnicas establecidas en un trabajo conjunto de C.-G. Li, M. Li y el autor [27], pueden ser aplicadas satisfactoriamente en el analisis de una clase amplia de ecuaciones fracionarias multi-termino degeneradas con derivadas de Caputo.