Comparative analysis of the fractional order Cahn-Allen equation
[ X ]
Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier B.V.
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This 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)
Açıklama
Anahtar Kelimeler
Caputo operator, Fractional-order Cahn-Allen equation, Laplace residual power series, Laplace transform
Kaynak
Partial Differential Equations in Applied Mathematics
WoS Q Değeri
Scopus Q Değeri
Q1
Cilt
8
