Hölder regularity for abstract semi-linear fractional differential equations in Banach spaces

Abstract

In the present work the optimal regularity, in the sense of Hölder continuity, of linear and semi-linear abstract fractional differential equations is investigated in the framework of complex Banach spaces. This framework has been considered by the authors as the most convenient to provide a posteriori error estimates for the time discretizations of such a kind of abstract differential equations. In the spirit of the classical a posteriori error estimates, under certain assumptions, the error is bounded in terms of computable quantities, in our case measured in the norm of Hölder continuous and weighted Hölder continuous functions.