Feasibility of variable delay fuzzy fractional stochastic differential system with non-instantaneous impulses

This paper explores the realm of dynamical control systems through fuzzy modelling, where the dynamics are shaped by a fuzzy stochastic process (FSP) propelled by fuzzy Brownian motion (FBM). Specifically, the paper introduces a new fractional stochastic differential equation (FSDE) featuring variab...

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Bibliographic Details
Published inApplied mathematics in science and engineering Vol. 33; no. 1
Main Authors Shalini, Manjitha Mani, Kandasamy, Banupriya, Rangasamy, Maheswari, Dhandapani, Prasantha Bharathi, Zeb, Anwar, Khan, Ilyas, Omer, Abdoalrahman S.A.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 31.12.2025
Subjects
Banach contraction principle
Caputo derivative
fuzzy Ito process
Fuzzy set theory
non-instantaneous impulses
variable delay
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ISSN2769-0911
2769-0911
DOI10.1080/27690911.2025.2458612

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Summary:This paper explores the realm of dynamical control systems through fuzzy modelling, where the dynamics are shaped by a fuzzy stochastic process (FSP) propelled by fuzzy Brownian motion (FBM). Specifically, the paper introduces a new fractional stochastic differential equation (FSDE) featuring variable fuzzy delays and non-instantaneous impulses driven by FBM. The study attempts to ascertain whether global and local solutions for the suggested system exist and are unique by applying fuzzy metrics and Banach contraction mapping principle. The efficacy of the analytical findings is demonstrated through a pertinent example.
ISSN:2769-0911
2769-0911
DOI:10.1080/27690911.2025.2458612