Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

This article is devoted to examine the exponential behavior of stochastic FitzHugh–Nagumo equation in Hilbert space. Initially, the proposed model is reformulated into an space, and the existence of mild solution is constructed by employing Mönch fixed‐point theorem and Hausdorff measure of non‐comp...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 46; no. 8; pp. 9589 - 9604
Main Authors Durga, N., Malik, Muslim
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.05.2023
Subjects
Brownian motion
existence of solution
Existence theorems
exponential stability
FitzHugh–Nagumo equation
fractional Brownian motion
Hilbert space
non‐instantaneous impulse
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Summary:This article is devoted to examine the exponential behavior of stochastic FitzHugh–Nagumo equation in Hilbert space. Initially, the proposed model is reformulated into an space, and the existence of mild solution is constructed by employing Mönch fixed‐point theorem and Hausdorff measure of non‐compactness. Furthermore, suitable conditions are developed to prove the proposed model's exponential behavior which reflects the stable generation and transmission of electric signal in neurons. At last, an example is presented to verify the established theoretical concepts.
Bibliography:Funding information
Science and Engineering Research Board, DST, Govt. of India, SPG Project File No. SPG/2021/002891.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9076