Jarad, FahdBourchi, SoumiaAbdeljawad, ThabetJarad, FahdAdjabi, YassineAbdeljawad, ThabetMahariq, Ibrahim2024-01-172024-01-172023Bourchi, Soumia;...et.al. (2023). "On abstract Cauchy problems in the frame of a generalized Caputo type derivative", Advances in the Theory of Nonlinear Analysis and its Applications, Vol.7, No.1, pp.1-28.25872648https://hdl.handle.net/20.500.12416/6906In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results.eninfo:eu-repo/semantics/openAccessAbstract Cauchy ProblemCaputo Type Generalized Fractional OperatorsContinuous Dependence On ParametersExistenceFixed Point TheoremsMittag-Leffler Type FunctionStabilityUniformly Continuous SemigroupsUniquenessArticle7112810.31197/atnaa.1147950