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Keywords = ν -caputo fractional system

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16 pages, 329 KiB  
Article
Finite-Approximate Controllability of ν-Caputo Fractional Systems
by Muath Awadalla, Nazim I. Mahmudov and Jihan Alahmadi
Fractal Fract. 2024, 8(1), 21; https://doi.org/10.3390/fractalfract8010021 - 26 Dec 2023
Cited by 2 | Viewed by 1516
Abstract
This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν-Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν-Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control [...] Read more.
This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν-Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν-Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control strategy that not only satisfies the approximative controllability property but also ensures exact finite-dimensional controllability. Leveraging the approximative controllability of the corresponding linear ν-Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear ν-Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to ν-Caputo fractional heat equations. Full article
(This article belongs to the Special Issue Mathematical and Physical Analysis of Fractional Dynamical Systems)
18 pages, 337 KiB  
Article
On ν-Level Interval of Fuzzy Set for Fractional Order Neutral Impulsive Stochastic Differential System
by Manjitha Mani Shalini, Nazek Alessa, Banupriya Kandasamy, Karuppusamy Loganathan and Maheswari Rangasamy
Mathematics 2023, 11(9), 1990; https://doi.org/10.3390/math11091990 - 23 Apr 2023
Cited by 3 | Viewed by 1351
Abstract
The main concern of this paper is to investigate the existence and uniqueness of a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by fuzzy Brownian motion using fuzzy numbers with bounded ν-level intervals that are convex, normal and [...] Read more.
The main concern of this paper is to investigate the existence and uniqueness of a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by fuzzy Brownian motion using fuzzy numbers with bounded ν-level intervals that are convex, normal and upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality and the Banach fixed-point theorem are employed to probe the local and global existence. An analytical example is provided to examine the theoretical results. Full article
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