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On the new concept of solutions and existence results for impulsive fractional evolution equations. (English) Zbl 1264.34014
The paper is concerned with the existence of PC-mild solutions for Cauchy problems for impulsive fractional evolution equations involving the Caputo fractional derivative. The paper is organised as follows: following preliminaries, in which the authors introduce the notations and review existing literature, the authors present the concept of the PC-mild solution. They provide existence results for impulsive Cauchy problems and for impulsive nonlocal Cauchy problems and conclude the paper with some examples to illustrate the theory.

MSC:
34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
47J35 Nonlinear evolution equations
34G20 Nonlinear differential equations in abstract spaces
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