EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES

doi:10.1007/s10473-025-0412-3

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1471-1481.doi: 10.1007/s10473-025-0412-3

EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES

Shengda ZENG^1,*, Abderrahim BOUACH², Tahar HADDAD³

1. National Center for Applied Mathematics in Chongqing, and School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;
2. Laboratoire LITAN Ecole supérieure en Sciences et Technologies de l'Informatique et du Numérique RN 75, Amizour 06300, Bejaia, Algérie;
3. Laboratoire LMPEA, Faculté des Sciences Exactes et Informatique, Université Mohammed Seddik Benyahia, Jijel, B. P. 98, Jijel 18000, Algérie

收稿日期:2024-04-11 修回日期:2024-08-29 出版日期:2025-10-10 发布日期:2025-10-10

EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES

Shengda ZENG^1,*, Abderrahim BOUACH², Tahar HADDAD³

1. National Center for Applied Mathematics in Chongqing, and School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;
2. Laboratoire LITAN Ecole supérieure en Sciences et Technologies de l'Informatique et du Numérique RN 75, Amizour 06300, Bejaia, Algérie;
3. Laboratoire LMPEA, Faculté des Sciences Exactes et Informatique, Université Mohammed Seddik Benyahia, Jijel, B. P. 98, Jijel 18000, Algérie

Received:2024-04-11 Revised:2024-08-29 Online:2025-10-10 Published:2025-10-10
Contact: ^*Shengda ZENG, E-mail: shengdazeng@gmail.com
About author:Abderrahim BOUACH, E-mail: abderrahimbouach@gmail.com; Tahar HADDAD, E-mail: haddadtr2000@yahoo.fr
Supported by:
Natural Science Foundation of Guangxi (2021GXNSFFA196004, 2024GXNSFBA010337), the NNSF of China (12371312), the Natural Science Foundation of Chongqing (CSTB2024NSCQ-JQX0033). It was also supported by the project cooperation between Guangxi Normal University and Yulin Normal University.

摘要/Abstract

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.

关键词: fractional differential inclusion, Moreau's sweeping process, prox-regular sets, fixed point

Abstract: 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.

Key words: fractional differential inclusion, Moreau's sweeping process, prox-regular sets, fixed point

Shengda ZENG, Abderrahim BOUACH, Tahar HADDAD. EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES[J]. 数学物理学报(英文版), 2025, 45(4): 1471-1481.

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.

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EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES

EXISTENCE RESULT FOR FRACTIONAL STATE-DEPENDENT SWEEPING PROCESSES

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