doi:10.1002/mana.201800342engAbadias, L.Alvarez, E.Fractional Cauchy problem with memory effectsART-2020-118839We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects (Formula presented.) where (Formula presented.) and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study global or blow up mild solutions when the nonlinearity f satisfies a locally Lipschitz condition. The case of critical nonlinearities is also treated.2020http://zaguan.unizar.es/record/13078410.1002/mana.201800342http://zaguan.unizar.es/record/130784oai:zaguan.unizar.es:130784info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MCYTS-MTM2016-77710-PMathematische Nachrichten 293 (2020), 1846-1872All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/closedAccess