Opuscula Math. 31, no. 3 (2011), 341-357
http://dx.doi.org/10.7494/OpMath.2011.31.3.341
Opuscula Mathematica
On nonlocal problems for fractional differential equations in Banach spaces
XiWang Dong
JinRong Wang
Yong Zhou
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.
- XiWang Dong
- Guizhou University, Department of Mathematics, Guiyang, Guizhou 550025, P.R. China
- JinRong Wang
- Guizhou University, Department of Mathematics, Guiyang, Guizhou 550025, P.R. China
- Yong Zhou
- Xiangtan University, Department of Mathematics, Xiangtan, Hunan 411105, P.R. China
- Received: 2010-11-20.
- Revised: 2010-12-09.
- Accepted: 2010-12-10.
