@misc{10498/38911,
year = {2026},
month = {3},
url = {http://hdl.handle.net/10498/38911},
abstract = {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.},
publisher = {Springer Nature},
keywords = {Well-posedness},
keywords = {block operator matrix},
keywords = {systems of nonlocal partial differential equations},
keywords = {vector-valued H¨older spaces},
keywords = {tempered fractional derivatives},
title = {Well-posedness of time-fractional systems in vector-valued Hölder spaces},
doi = {10.1007/s00028-026-01189-8},
author = {Alvarez, Edgardo and Lizama, Carlos and Murillo Arcila, Marina},
}