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RESEARCH ARTICLE

Ulam's stability of neutral fractional stochastic differential equation with the application of homeostasis circuit

Mattuvarkuzhali Chandrasekaran1 ,  Elavarasan Krishnasamy2 ,  Pongthep Poungthong3* ,  An Youdan4,5
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1 Department of Mathematics, Vel Tech Multi Tech Dr Rangarajan Dr Sakunthala Engineering College, Tamil Nadu, India
2 Department of Mathematics Vel Tech Rangarajan Dr Sagunthala R & D Institute of Science and Technology, Tamil Nadu, India
3 Department of Industrial Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
4 Faculty of Education, Shinawatra University, Pathum Thani, Thailand
5 Faculty of Economics, Guizhou Qannan Economic College, Guizhou, China
IJOCTA, 026210088 https://doi.org/10.36922/IJOCTA026210088
Received: 22 May 2026 | Revised: 8 August 2026 | Accepted: 10 August 2026 | Published online: 26 August 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

In this paper, Ulam’s stability of neutral fractional stochastic differential equations (NFSDEs) with sub-fractional Brownian motion (sfBm) is studied. Existence and stability results are established using fixed point theory, semigroup theory, and fractional calculus in a stochastic setting. We modify unstable impulses into stable impulses in the signal transformation of the cell tissue trajectory. Numerical simulations are provided to verify the obtained results. Fractional components are used to construct a fractional-order analogue circuit model for an artificial tissue homeostasis circuit, which is relevant to the application features. The proposed circuit offers several advantages for framing effective cell populations, including (i) predicting the death of β cells at the microscopic level for type 1 diabetics, (ii) regenerating the dead cells through stem cells, and (iii) achieving stable signal transformation between β cells and stem cells.

Keywords
Fractional differential equation
Ulam’s stability
Stochastic calculus
Non-instantaneous impulse
Homeostatis analog circuit
Health sytem modelling
Sustainable innovation
SDG 3
Funding
None.
Conflict of interest
The authors declare that they have no conflict of interest.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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