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A novel numerical method for stochastic conformable fractional differential systems

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Bibliographic Details
Title: A novel numerical method for stochastic conformable fractional differential systems
Authors: Aisha F. Fareed, Emad A. Mohamed, Mokhtar Aly, Mourad S. Semary
Source: AIMS Mathematics, Vol 10, Iss 3, Pp 7509-7525 (2025)
Publisher Information: American Institute of Mathematical Sciences (AIMS), 2025.
Publication Year: 2025
Subject Terms: fractional-order systems, QA1-939, conformable derivative, population model, white noise, stochastic differential equations, Mathematics
Description: This study introduced the conformable fractional discrete Temimi–Ansari method (CFDTAM), a novel numerical framework designed to solve fractional stochastic nonlinear differential equations with enhanced efficiency and accuracy. By leveraging the conformable fractional derivative (CFD), the CFDTAM unifies classical and fractional-order systems while maintaining computational simplicity. The method's efficacy was demonstrated through applications to a stochastic population model and the Brusselator system, showcasing its ability to handle nonlinear dynamics with high precision. A comprehensive convergence analysis was also conducted to validate the reliability and stability of the proposed method. All computations were performed using Mathematica 12 software, ensuring accuracy and consistency in numerical simulations. CFDTAM sets a new benchmark in fractional stochastic modeling, paving the way for advancements in partial differential equations, delay systems, and hybrid models.
Document Type: Article
ISSN: 2473-6988
DOI: 10.3934/math.2025345
Access URL: https://doaj.org/article/ebd0565e26d14b4bad38a207b5cdb10f
Accession Number: edsair.doi.dedup.....752acc7d5dcd81e17e65b307da82563f
Database: OpenAIRE
Description
Abstract:This study introduced the conformable fractional discrete Temimi–Ansari method (CFDTAM), a novel numerical framework designed to solve fractional stochastic nonlinear differential equations with enhanced efficiency and accuracy. By leveraging the conformable fractional derivative (CFD), the CFDTAM unifies classical and fractional-order systems while maintaining computational simplicity. The method's efficacy was demonstrated through applications to a stochastic population model and the Brusselator system, showcasing its ability to handle nonlinear dynamics with high precision. A comprehensive convergence analysis was also conducted to validate the reliability and stability of the proposed method. All computations were performed using Mathematica 12 software, ensuring accuracy and consistency in numerical simulations. CFDTAM sets a new benchmark in fractional stochastic modeling, paving the way for advancements in partial differential equations, delay systems, and hybrid models.
ISSN:24736988
DOI:10.3934/math.2025345