A discussion of Newton's law of cooling using difference equations in fuzzy frames as an alternative to the traditional continuous dynamical system

Abdul Alamin, Mostafijur Rahaman, Soheil Salahshour, Sankar Prasad Mondal, Shariful Alam, Kamal Hossain Gazi and Md. Jahangir Mian

International Journal of Mathematics in Operational Research, 2026, vol. 34, issue 3, 287-308

Abstract: This study, a notable one in the field of heat transfer, adapts a discrete and continuous heat transfer model in a fuzzy environment using fuzzy assumptions. This model was developed using the idea of discrete actual observation data and explored using a fuzzy framework in an effort to thoroughly analyse the experiments on natural occurrences. Using the Hukuhara difference notion, fuzzy arithmetic and difference calculus approach, fuzzy solutions to the governing model are demonstrated. In order to visualise the graphical solution and for usefulness to the suggested approaches, experimental data (both in crisp and fuzzy) of heat transfer of a hot glass of 40 ml water is taken in Newton's law of cooling. In discrete fuzzy frame Newton's law of cooling gives stable solution for some α ϵ [0, 1] and significant outcomes are observed from graphical solutions.

Keywords: Hukuhara difference; fuzzy difference equation; Newton's law of cooling. (search for similar items in EconPapers)
Date: 2026
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