Mieczyslaw CichonIreneusz KubiaczykAneta Sikorska-NowakAhmet YantirYantir, AhmetCichon, MieczyslawKubiaczyk, IreneuszSikorska-Nowak, Aneta2025-10-0620120420-12132391-4661https://gcris.yasar.edu.tr/handle/123456789/7076In this paper we obtain the existence of solutions and Caratheodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales x(triangle)(t) = f(tx(t)) x(0)=x(o) t is an element of I-a where f is continuous or f satisfies Caratheodory conditions and some conditions expressed in terms of measures of noncompactness. The Manch fixed point theorem is used to prove the main result which extends these obtained for real valued functions.Englishinfo:eu-repo/semantics/openAccessCauchy dynamic problem, Banach space, measure of non-compactness, Caratheodory solutions, time scalesDIFFERENTIAL-EQUATIONS, DISCRETE EQUATIONS, TIME SCALESTime ScalesBanach SpaceCauchy Dynamic ProblemCaratheodory SolutionsMeasure of Non-CompactnessArticle