Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

Charles Castaing, Christiane Godet-Thobie and Le Xuan Truong
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Charles Castaing: Département de Mathématiques, Université Montpellier II, Case Courrier 051, 34095 Montpellier CEDEX 5, France
Christiane Godet-Thobie: Laboratoire de Mathématiques de Bretagne Atlantique, Université de Bretagne Occidentale, CNRS UMR 6205, 6, Avenue Victor Le Gorgeu, CS 9387, F-29238 Brest CEDEX 3, France
Le Xuan Truong: Department of Mathematics and Statistics, University of Economics Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam

Mathematics, 2020, vol. 8, issue 9, 1-30

Abstract: This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.

Keywords: fractional differential inclusion; maximal monotone operator; Riemann–Liouville integral; absolutely continuous in variation; Vladimirov pseudo-distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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