engAbadías Ullod, LucianoÁlvarez, EdgardoUniform stability for fractional Cauchy problems and applicationsART-2018-106684In this paper we give uniform stable spatial bounds for the resolvent operator fami- lies of the abstract fractional Cauchy problem on R+. Such bounds allow to prove existence and uniqueness of µ-pseudo almost automorphic e-mild regular solutions to the nonlinear fractional Cauchy problem in the whole real line. Finally, we apply our main results to the fractional heat equation with critical nonlinearities.2018http://zaguan.unizar.es/record/71091http://zaguan.unizar.es/record/71091oai:zaguan.unizar.es:71091info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-PTopological Methods in Nonlinear Analysis by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess