Opuscula Math. 30, no. 3 (2010), 361-381
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.
- Received: 2010-02-09.
- Revised: 2010-03-20.
- Accepted: 2010-04-08.