Discrete almost maximal regularity and stability for fractional differential equations in Lp([0, 1], Ω)

Li Liu, Zhenbin Fan, Gang Li and Sergey Piskarev

Applied Mathematics and Computation, 2021, vol. 389, issue C

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 Grünwald-Letnikov approximation for the fractional derivative, the discrete almost maximal regularity and stability of the implicit difference scheme in Lτnp([0,1],Ωn) 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 Lτnp([0,1],Ωn) spaces are achieved as well.

Keywords: Fractional evolution equation; Discrete almost maximal regularity; Stability; Resolvent family; Finite difference method (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305300

DOI: 10.1016/j.amc.2020.125574

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