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

In the present work the optimal regularity, in the sense of Holder 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 Holder continuous and weighted Holder continuous functions.

Automated summary

The study investigated the optimal regularity in terms of Holder continuity of linear and semi-linear abstract fractional differential equations in the framework of complex Banach spaces for providing a posteriori error estimates. The error can be bounded in terms of computable quantities, measured in the norm of Holder continuous and weighted Holder continuous functions, under certain assumptions.