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<p>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 <i>state-dependent</i>. 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 <i>C</i> is <i>independent</i> of the state <i>u</i> (i.e. <i>C</i>:= <i>C</i>(<i>t</i>), as presented in [22, 23]), we prove the existence of a solution to our quasi-variational fractional sweeping process in <i>infinite-dimensional</i> 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.</p>

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Existence result for fractional state-dependent sweeping processes

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Shengda Zeng,
  • Abderrahim Bouach,
  • Tahar Haddad

摘要

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.