Discrete almost maximal regularity and stability for fractional differential equations in L-p([0,1], Omega)

摘要

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-tau n(p) ([0,1], Omega(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-tau n(p) ([0,1], Omega(n)) spaces are achieved as well. (C) 2020 Elsevier Inc. All rights reserved.