Abstract The present paper is devoted to the study of discrete almost maximal regularity and stability of the difference schemes of nonhomogeneous fractional evolution equations. Using the discretization method of the fractional derivative proposed by Ashyralyev, which actually is the same as the Grunwald-Letnikov approximation for the fractional derivative, the discrete almost maximal regularity and stability of the implicit difference scheme in L τ n p ( [ 0 , 1 ] , Ω n ) spaces are established. For the explicit difference scheme, the expression of the solution is obtained. Then the discrete almost maximal regularity and stability of the explicit difference scheme in L τ n p ( [ 0 , 1 ] , Ω n ) spaces are achieved as well.

中文翻译：

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L([0, 1], Ω) 中分数阶微分方程的离散几乎最大正则性和稳定性

摘要 本文致力于研究非齐次分数阶演化方程差分格式的离散近似极大正则性和稳定性。利用Ashyralyev提出的分数阶导数的离散化方法，实际上与分数阶导数的Grunwald-Letnikov近似相同，隐式差分格式在L τ np ( [ 0 , 1 ] , Ω n ) 空间成立。对于显式差分方案，得到了解的表达式。然后也实现了 L τ np ( [ 0 , 1 ] , Ω n ) 空间中显式差分方案的离散几乎最大正则性和稳定性。