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C-RESOLVENT FAMILIES IN LOCALLY CONVEX SPACES
Published in Marko Kostić, Abstract Volterra Integro-Differential Equations, 2015
where A is a closed densely defined operator on a complex Banach space E, Dat denotes the operator valued Riemann-Liouville fractional derivative of order a e (1, 2), x e E and f : (0, œ) E. In order to do that, the authors have introduced in [257, Definition 3.1] the notion of an a-order fractional resolvent (T(t))t 0. We
(ω, c)-periodic and asymptotically (ω, c)-periodic mild solutions to fractional Cauchy problems
Published in Applicable Analysis, 2023
James Larrouy, Gaston M. N'Guérékata
The aim of this paper is to keep on investigating properties of -periodic and asymptotically -periodic functions and their applications to the following equations: and were stands for the Caputo derivative and A is a linear densely defined operator of sectorial type on a complex Banach space , and the function is -periodic or asymptotically -periodic with respect to the first variable. Our main results are Theorems 3.2, 3.5 and 3.7.
A new existence theory for periodic solutions to evolution equations
Published in Applicable Analysis, 2020
Khalil Ezzinbi, Mohamed Aziz Taoudi
Let be a densely defined operator on a Banach space Z. The essential spectrum of denoted by is the set of such that one of the following conditions holds: is not closed,the generalized eigenspace is of infinite dimension,λ is a limit point of .
Bohr-Neugebauer property for almost automorphic partial functional differential equations
Published in Applicable Analysis, 2019
Brahim Es-sebbar, Khalil Ezzinbi, Gaston M. N’Guérékata
[42]] Let be a densely defined operator on a Banach space Y. Let denote the spectrum of the operator . The essential spectrum of denoted by is the set of such that one of the following conditions holds: is not closed,the generalized eigenspace is of infinite dimension, is a limit point of The essential radius of is defined by