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Summer 2020 Square-mean almost automorphic solution of a stochastic cellular neural network on time scales
Soniya Dhama, Syed Abbas
J. Integral Equations Applications 32(2): 151-170 (Summer 2020). DOI: 10.1216/jie.2020.32.151

Abstract

We derive some sufficient conditions for the existence of a square-mean almost automorphic solution for a stochastic cellular neural network on time scales by using Krasnoselskii’s fixed point theorem. The Banach contraction principle is also used to show the uniqueness of a solution with some additional restrictions. Exponential stability of the obtained solution is also discussed by taking a suitable Lyapunov functional on time scale. At the end, we give a numerical example to illustrate the effectiveness of the obtained theoretical results. Our results are valid for general time scale, and the cases 𝕋=ℝ or ℤ are particular cases.

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Soniya Dhama. Syed Abbas. "Square-mean almost automorphic solution of a stochastic cellular neural network on time scales." J. Integral Equations Applications 32 (2) 151 - 170, Summer 2020. https://doi.org/10.1216/jie.2020.32.151

Information

Received: 2 August 2018; Accepted: 22 June 2019; Published: Summer 2020
First available in Project Euclid: 28 August 2020

zbMATH: 07282581
MathSciNet: MR4141402
Digital Object Identifier: 10.1216/jie.2020.32.151

Subjects:
Primary: 34N05, 43A60

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 2 • Summer 2020
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