Opuscula Math. 30, no. 3 (), 361-381
http://dx.doi.org/10.7494/OpMath.2010.30.3.361
Opuscula Mathematica

# Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces

Abstract. In this paper, we study the existence and uniqueness of the $$PC$$-mild solution for a class of impulsive fractional differential equations with time-varying generating operators and nonlocal conditions. By means of the generalized Ascoli-Arzela Theorem given by us and the fixed point theorem, some existence and uniqueness results are obtained. Finally, an example is given to illustrate the theory.
Keywords: nonlocal conditions, impulsive equations, fractional differential equations, time-varying generating operators, $$PC$$-mild solution.
Mathematics Subject Classification: 34G10, 34G20.