The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke's subdifferential. (March 2023)

• Record Type: Journal Article
• Authors: Upadhyay, Anjali; Kumar, Surendra
• Is Part Of: Chaos, solitons and fractals. Volume 168(2023)
• Publication Date: 2023-03
• Subjects: 34K37 -- 34K50 -- 35R60 -- 93D23; Multi-term fractional system -- Clarke's generalized subdifferential -- Resolvent operator -- Rosenblatt process -- Stochastic inclusions -- Mild solution -- Exponential stability; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2023.113202
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This study explores a new class of stochastic multi-term fractional differential inclusions with the Clarke subdifferential involving the Rosenblatt process. The presence and uniqueness of a solution are determined by the successive approximation approach in combination with the stochastic analysis methodology and the resolvent operators. Furthermore, new sufficient conditions are given to ensure the exponential decay of the mild solution without Lipschitz conditions on non-linear terms. We have also provided an example to validate the obtained results.