https://doi.org/10.1140/epjp/s13360-025-06908-7
Review
Fuzzy reaction–diffusion problems solved by homotopy perturbation method
Department of Mathematics, Vellore Institute of Technology, 600 127, Chennai, India
Received:
8
December
2024
Accepted:
27
September
2025
Published online:
31
October
2025
This study applies the Homotopy Perturbation Method (HPM) to solve fuzzy reaction–diffusion equations in both linear and nonlinear forms, addressing uncertainties in diffusion–advection parameters. Such equations are vital in modeling diverse systems in science and engineering. HPM offers a modern analytical approach to simplify these complex problems, with its effectiveness demonstrated through several fuzzy reaction–diffusion examples. Applications include drug transport and tumour growth in biological engineering, pollutant dispersion in environmental science, and heat or particle diffusion in materials science, where precise parameters are often unknown. By integrating fuzzy uncertainty into reaction–diffusion modeling and efficiently solving it with HPM, this work provides a more realistic representation of systems affected by imprecise or uncertain parameters.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
