On a class of abstract degenerate fractional differential equations of parabolic type

Kostić, Marko

doi:10.14712/1213-7243.2015.235

Cited by 1 publication

(1 citation statement)

References 18 publications

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“…Unfortunately, this fact is not sufficiently enough for taking up a fairly complete study of the abstract degenerate Cauchy problems that are subordinated to those appearing in the above-mentioned examples and, concerning this question, we will only want to mention that the subordination fractional operator families can be constructed since the semigroups considered in [17, Chapter III] have a removable singularity at zero (cf. the proof of [5, Theorem 3.1], [47] and the forthcoming monograph [38] for more details). On the other hand, from the point of view of possible applications of Theorem 5.22, it is very important to know that the operators AB −1 or B −1 A generate exponentially bounded, analytic integrated semigroups.…”

Section: Multivalued Linear Operators As Subgenerators Of (A K)-regul...mentioning

confidence: 99%

Abstract degenerate Volterra inclusions in locally convex spaces

Kostic

2023

ejde

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In this paper, we analyze the abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces by using multivalued linear operators and vector-valued Laplace transform. We follow the method which is based on the use of (a, k)-regularized C-resolvent families generated by multivalued linear operators and which suggests a very general way of approaching abstract Volterra equations. Among many other themes, we consider the Hille-Yosida type theorems for $(a, k)$-regularized C-resolvent families, differential and analytical properties of $(a, k)$-regularized $C$-resolvent families, the generalized variation of parameters formula, and subordination principles. We also introduce and analyze the class of $(a, k)$-regularized $(C_1,C_2)$-existence and uniqueness families. The main purpose of third section, which can be viewed of some independent interest, is to introduce a relatively simple and new theoretical concept useful in the analysis of operational properties of Laplace transform of non-continuous functions with values in sequentially complete locally convex spaces. This concept coincides with the classical concept of vector-valued Laplace transform in the case that $X$ is a Banach space. For more information see https://ejde.math.txstate.edu/Volumes/2023/63/abstr.html

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Section: Multivalued Linear Operators As Subgenerators Of (A K)-regul...mentioning

confidence: 99%