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A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
Uniform continuity over locally compact quantum groups
We define, for a locally compact quantum group in the sense of
Kustermans--Vaes, the space of of left uniformly continuous elements
in . This definition covers both the usual left uniformly
continuous functions on a locally compact group and Granirer's uniformly
continuous functionals on the Fourier algebra. We show that is an
operator system containing the -algebra and contained in its
multiplier algebra . We use this to partially answer an open problem
by Bedos--Tuset: if is co-amenable, then the existence of a left invariant
mean on is sufficient for to be amenable. Furthermore, we study
the space of weakly almost periodic elements of : it is a
closed operator system in containing and--for
co-amenable --contained in . Finally, we show that--under certain
conditions, which are always satisfied if is a group--the operator system
is a -algebra.Comment: 22 pages; some nip and tuc
Operator splittings and spatial approximations for evolution equations
The convergence of various operator splitting procedures, such as the
sequential, the Strang and the weighted splitting, is investigated in the
presence of a spatial approximation. To this end a variant of Chernoff's
product formula is proved. The methods are applied to abstract partial delay
differential equations.Comment: to appear in J. Evol. Equations. Reviewers comments are incorporate
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