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Nonlocal Cauchy problem for fractional evolution equations. (English) Zbl 1260.34017
Summary: The nonlocal Cauchy problem is discussed for fractional evolution equations in an arbitrary Banach space and various criteria for the existence and uniqueness of mild solutions are obtained. An example to illustrate the applications of main results is also given.

##### MSC:
 34A08 Fractional ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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