This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints. The values of the moving set are time and state-dependent. The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem. By combining Schauder's fixed point theorem with a well-posedness theorem when the set $ C $ is independent of the state $u$ (i.e. $C := C(t)$, as presented in [22, 23]), we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces. Similar to the conventional state-dependent sweeping process, achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
Shengda ZENG
,
Abderrahim BOUACH
,
Tahar HADDAD
. EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES[J]. Acta mathematica scientia, Series B, 2025
, 45(4)
: 1471
-1481
.
DOI: 10.1007/s10473-025-0412-3
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