THERMAL SCIENCE

International Scientific Journal

Lei ZhaoORCID

,

Ya Chen

,

Ji-Huan He

FRACTIONAL CALCULUS INNOVATIONS AND MACHINE LEARNING-DRIVEN ADVANCES IN THERMAL SCIENCE

ABSTRACT
This paper explores fractional calculus innovations and machine learning's role in advancing thermal science, especially in smart textiles. It first introduces three key fractional derivatives (Caputo, Riemann-Liouville, two-scale fractal) for thermal analysis, highlighting their strengths in capturing non-locality, memory effects, and fractal characteristics. Then, it details how the two-scale fractal deriva-tive modifies Caputo and Riemann-Liouville derivatives to better model complex thermal systems in smart textiles, with simplified forms balancing accuracy and computational efficiency. Finally, it discusses machine learning's synergy with fractional calculus, optimizing model parameters, capturing nonlinearities, and enabling data-driven fractional models, to solve intractable thermal problems in smart textiles, supporting applications like complex textile material heat transfer and electronic thermal management in wearable smart textiles.
KEYWORDS
fractional calculus, two-scale fractal derivative, modified fractional derivatives, machine learning, mems, wearable sensors, smart textiles
PAPER SUBMITTED: 2025-03-05
PAPER REVISED: 2025-10-10
PAPER ACCEPTED: 2025-10-10
PUBLISHED ONLINE: 2026-04-12
DOI REFERENCE: https://doi.org/10.2298/TSCI2602805Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2026, VOLUME 30, ISSUE No. 2, PAGES [805 - 814]
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Fractional calculus innovations and machine learning-driven advances in thermal science

© 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-NonCommercial-NoDerivs 4.0 International licence