doi:10.12775/TMNA.2018.038engAbadias, L.Álvarez, E.Uniform stability for fractional cauchy problems and applicationsART-2018-110331¿In this paper we give uniform stable spatial bounds for the resolvent operator families 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/13076310.12775/TMNA.2018.038http://zaguan.unizar.es/record/130763oai:zaguan.unizar.es:130763info:eu-repo/grantAgreement/ES/MCYTS/DGI-FEDERinfo:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-PTopological Methods in Nonlinear Analysis 52, 2 (2018), 707-728All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/closedAccess