Hyers–Ulam stability for a class of Hadamard fractional Itô–Doob stochastic integral equations. (January 2023)

• Record Type: Journal Article
• Authors: Kahouli, Omar; Ben Makhlouf, Abdellatif; Mchiri, Lassaad; Rguigui, Hafedh
• Is Part Of: Chaos, solitons and fractals. Volume 166(2023)
• Publication Date: 2023-01
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112918
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Our goal in this work is to demonstrate the existence and uniqueness of the solution to a class of Hadamard Fractional Itô–Doob Stochastic integral equations (HFIDSIE) of order φ ∈ ( 0, 1 ) via the fixed point technique (FPT). Hyers–Ulam stability (HUS) is investigated for HFIDSIE according to the Gronwall inequality. Two theoretical examples are provided to illustrate our results. Highlights: The existence of solutions of Hadamard Fractional Itô–Doob Stochastic integral equations is studied. The Ulam–Hyers stability of Hadamard Fractional Itô–Doob Stochastic integral equations is given. Two examples are provided to show the validity of the theoretical results.