Nonlocal Cauchy problems governed by compact operator families

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EXISTENCE OF SOLUTIONS OF ABSTRACT FRACTIONAL IMPULSIVE SEMILINEAR EVOLUTION EQUATIONS (2010, background): “Subsequently several authors have investigated the problem for different types of nonlinear differential equations and integrodifferential equations including functional differential equations in Banach spaces [2-4, 10, 20].”
Approximate Controllability of Second-Order Evolution Differential Inclusions in Hilbert Spaces (2015, background): “Existence and controllability results of nonlinear differential equations and fractional differential equations with nonlocal conditions have been studied by several authors for different kind of problems [2,3,15,18,23,29,34,56].”
The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces (2010, background): “Subsequently several authors discussed the problem for different kinds of nonlinear differential equations and integrodifferential equations including functional differential equations in Banach spaces [17] [18] [19].”
Monotone Iterative Technique for a Class of Semilinear Evolution Equations with Nonlocal Conditions (2013, background): “1) can not be solved by the results in [2,4,12,13].”