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The normalized time-fractional Cahn–Hilliard equation

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  • Lee, Hyun Geun
  • Kwak, Soobin
  • Ham, Seokjun
  • Hwang, Youngjin
  • Kim, Junseok

Abstract

We present a normalized time-fractional Cahn–Hilliard (TFCH) equation by incorporating time-fractional derivatives to model memory effects in phase separation processes. We use a normalized time-fractional derivative, which is a form of the Caputo fractional derivative, to improve the flexibility and physical interpretation of the model. This normalization allows for a more consistent interpretation of fractional orders, which enables fair comparisons across different orders of the derivative. To solve the normalized TFCH equation, we use an efficient computational scheme based on the Fourier spectral method, which ensures high accuracy and computational efficiency. Furthermore, we conduct a thorough investigation into the dynamic behavior of the normalized TFCH equation and focus on how varying the fractional-order time derivative influences the evolution and morphology of phase domains. Numerical simulations demonstrate the versatility and effectiveness of the proposed method in modeling complex phase separation dynamics.

Suggested Citation

  • Lee, Hyun Geun & Kwak, Soobin & Ham, Seokjun & Hwang, Youngjin & Kim, Junseok, 2025. "The normalized time-fractional Cahn–Hilliard equation," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925004631
    DOI: 10.1016/j.chaos.2025.116450
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    References listed on IDEAS

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    1. Calatayud, Julia & Jornet, Marc & Pinto, Carla M.A., 2024. "On the interpretation of Caputo fractional compartmental models," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. Bae, Hantaek, 2023. "Global existence of unique weak solutions and decay rates of Active model B with the logarithmic Cahn–Hilliard equation in Wiener space," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Sungha Yoon & Darae Jeong & Chaeyoung Lee & Hyundong Kim & Sangkwon Kim & Hyun Geun Lee & Junseok Kim, 2020. "Fourier-Spectral Method for the Phase-Field Equations," Mathematics, MDPI, vol. 8(8), pages 1-36, August.
    4. Zhang, Haiqing & Liao, Hong-lin, 2024. "High-order energy stable variable-step schemes for the time-fractional Cahn–Hilliard model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 171-182.
    5. Ran, Maohua & Zhou, Xiaoyi, 2021. "An implicit difference scheme for the time-fractional Cahn–Hilliard equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 61-71.
    6. Ren, Junjie & Lei, Hao & Song, Jie, 2024. "An improved lattice Boltzmann model for variable-order time-fractional generalized Navier-Stokes equations with applications to permeability prediction," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    7. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
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