Fractional sweeping process with Caputo type velocity constraint
Applicable Nonlinear Analysis, Volume 2, Issue 1, April 2025, Pages: 42–58
KECIS ILYAS
Laboratoire LMEPA, Faculté des Sciences Exactes et Informatique, Université Mohammed Seddik Benyahia, Jijel, B.P. 98, Jijel 18000, Algérie
HADDAD TAHAR
Laboratoire LMEPA, Faculté des Sciences Exactes et Informatique, Université Mohammed Seddik Benyahia, Jijel, B.P. 98, Jijel 18000, Algérie
ABDERRAHIM BOUACH
Laboratoire LITAN, École supérieure en Sciences et Technologies de l’Informatique et du Numérique, RN 75, Amizour 06300, Bejaia, Algérie
Abstract
This paper deals with the existence of solutions for a novel variant of fractional sweeping processes, where the Caputo type derivative belongs to the set of constraints which is assumed to be closed convex and varies in a Hölderian way. By using a modified catching-up algorithm, we construct a family of approximate solutions that converges to a Hölderian solution of the evolution inclusion under the semicoercivity condition of the considered operator. The Cauchy criterion of the approximate solutions in an infinite dimensional Hilbert space is obtained under some additional condition.
Cite this Article as
Kecis Ilyas, Haddad Tahar and Abderrahim Bouach, Fractional sweeping process with Caputo type velocity constraint, Applicable Nonlinear Analysis, 2(1), 42–58, 2025