Comparative analysis of the fractional order Cahn-Allen equation

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dc.contributor.authorKhan, Ibrar
dc.contributor.authorNawaz, Rashid
dc.contributor.authorAli, Ali Hasan
dc.contributor.authorAkgul, Ali
dc.contributor.authorLone, Showkat Ahmad
dc.date.accessioned2024-12-24T19:10:21Z
dc.date.available2024-12-24T19:10:21Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractThis current work presents a comparative study of the fractional-order Cahn-Allen (CA) equation, where the non-integer derivative is taken in the Caputo sense.The Cahn-Allen equation is an equation that assists in the comprehension of phase transitions and pattern formation in physical systems. This equation describes how different phases of matter, such as solids and liquids, change and interact throughout time. We employ two analytical methods: the Laplace Residual Power Series Method (LRPSM) and the New Iterative Method (NIM), to solve the proposed model. The LRPSM is a combination of the Laplace Transform and the Residual Power Series Method, while the New Iterative Method is a modified form of the Adomian Decomposition Method that does not require any type of polynomial or digitization. For the purpose of accuracy and reliability, we compare our findings with other methods and the exact solution used in the literature. Additionally, 2D and 3D plots are generated for various fractional order values denoted as p. These plots illustrate that as the fractional order p approaches 1, the graph of the approximate solution gradually coincides with the graph of the exact solution. © 2023 The Author(s)
dc.identifier.doi10.1016/j.padiff.2023.100576
dc.identifier.issn2666-8181
dc.identifier.scopus2-s2.0-85174056521
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org10.1016/j.padiff.2023.100576
dc.identifier.urihttps://hdl.handle.net/20.500.12604/4069
dc.identifier.volume8
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier B.V.
dc.relation.ispartofPartial Differential Equations in Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectCaputo operator
dc.subjectFractional-order Cahn-Allen equation
dc.subjectLaplace residual power series
dc.subjectLaplace transform
dc.titleComparative analysis of the fractional order Cahn-Allen equation
dc.typeArticle

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