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

Authors: Abdul Alamin; Mostafijur Rahaman; Soheil Salahshour; Sankar Prasad Mondal; Shariful Alam; Kamal Hossain Gazi; Md. Jahangir Mian

Addresses: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata – 741249, Nadia, India ' Department of Mathematics, School of Liberal Arts and Sciences, Mohan Babu University, Tirupati, Andhra Pradesh – 517102, India ' Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey; Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey; Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey ' Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata – 741249, Nadia, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah – 711103, West Bengal, India ' Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata – 741249, Nadia, India ' Lalgola Mahesh Narayan Academy, Lalgola – 742148, Murshidabad, West Bengal, India

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.

DOI: 10.1504/IJMOR.2026.155537

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.3, pp.287 - 308

Received: 29 May 2024
Accepted: 07 Aug 2024
Published online: 05 Aug 2026 *

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