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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:
34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
47J35Nonlinear evolution equations
34G20Nonlinear ODE in abstract spaces