%0 Journal Article 
%A Alvarez, Edgardo
%A Lizama, Carlos
%A Murillo Arcila, Marina
%T Well-posedness of time-fractional systems in vector-valued Hölder spaces
%D 2026
%@ 1424-3199
%U http://hdl.handle.net/10498/38911
%X We fully characterize the well-posedness in vector-valued Hölder in time spaces of a nonlocal
equation involving a closed operatormatrixAwith diagonal domain, defined on a product of Banach spaces,
solely in terms of the norm boundedness of a block-operator-valued symbol. We also give vector-valued
a priori maximal Hölder inequalities. Our result also contains a characterization in the case of a single
closed linear operator (not necessarily bounded), which is also new. We show that the condition that A is
the generator of an analytic semigroup is sufficient for the well-posedness. In particular, we show that the
well-posedness holds if the operators on the diagonal of A are generators of analytic semigroups and if the
off-diagonal entries satisfy a smallness condition. We exemplify our main results with abstract as well as
concrete models arising in fluid dynamics.
%K Well-posedness
%K block operator matrix
%K systems of nonlocal partial differential equations
%K vector-valued H¨older spaces
%K tempered fractional derivatives
%~ Universidad de Cádiz