Opuscula Math. 31, no. 3 (2011), 341-357
On nonlocal problems for fractional differential equations in Banach spaces
Abstract. In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Keywords: nonlocal problems, fractional differential equations, existence, generalized singular Gronwall inequality, fixed point method.
Mathematics Subject Classification: 26A33, 34K12, 34A40.
- Received: 2010-11-20.
- Revised: 2010-12-09.
- Accepted: 2010-12-10.