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THERMAL SCIENCE
International Scientific Journal
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A FRACTIONAL-ORDER NON-HOMOGENEOUS GREY BERNOULLI MODEL AND ITS APPLICATION
ABSTRACT
To study the gross regional product in Shizhong district, Leshan city, this paper developed a new grey forecasting model incorporating the non-homogeneous grey model and the fractional-order operator, abbreviated as FANGBM(1,1,k,c). Analytical expressions of the time response function, restored values, and system linear parameters are obtained by grey modelling theory and the least squares estimation method. The nonlinear parameters of the new model are determined by the whale optimization algorithm, which minimizes the mean absolute simulation percentage error. Furthermore, the FANGBM(1,1,k,c) model is applied to gross regional product in Shizhong district, and the results are compared with the GM(1,1), FAGM(1,1) and NGBM(1,1,k,c) models. The computational results show that the new model is suitable for studying the county economy.
KEYWORDS
fractional-order operator, non-homogeneous grey Bernoulli model, whale optimization algorithm, gross regional product
PAPER SUBMITTED: 2025-04-17
PAPER REVISED: 2025-09-23
PAPER ACCEPTED: 2025-12-12
PUBLISHED ONLINE: 2026-07-25
DOI REFERENCE: https://doi.org/10.2298/TSCI250417141Z
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© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International licence