Well-Posedness and Approximation for Nonhomogeneous Fractional Differential Equations. (15th June 2021) - Liu, Ru; Piskarev, Sergey
Abstract: In this paper, we consider the well-posedness and approximation for nonhomogeneous fractional differential equations in Banach spaces E . Firstly, we get the necessary and sufficient condition for the well-posedness of nonhomogeneous fractional Cauchy problems in the spaces C 0 β ( [ 0, T ] ; E ) . Secondly, by using implicit difference scheme and explicit difference scheme, we deal with the full discretization of the solutions of nonhomogeneous fractional differential equations in time variables, get the stability of the schemes and the order of convergence.