In this paper, a new scheme based on the exponential fitting technique is presented for solving the nonlinear time-fractional Swift-Hohenberg equation, where the first and second-order derivatives are replaced by Caputo fractional derivative. The exponential fitting technique depends on a parameter that led to getting high-order accuracy. The convergence and unconditional stability will be discussed using the Fourier method and the analysis is built on uniform and nonuniform time steps, to solve initial singularity by using the graded meshes. Applicability and theoretical results will be demonstrated and enhanced with numerical examples.

中文翻译：

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时间分数阶非线性Swift-Hohenberg方程：分析和数值模拟

提出了一种基于指数拟合技术的非线性时间分数维Swift-Hohenberg方程求解新方案，该方法将一阶和二阶导数替换为Caputo分数阶导数。指数拟合技术取决于导致获得高阶精度的参数。将使用傅立叶方法讨论收敛性和无条件稳定性，并基于均匀和非均匀时间步长进行分析，以使用渐变网格解决初始奇异性。数值示例将说明和增强适用性和理论结果。