Opuscula Math. 31, no. 4 (2011), 629-643
Existence and uniqueness results for fractional differential equations with boundary value conditions
Abstract. In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.
Keywords: fractional differential equations, boundary value conditions, singular Gronwall inequality, existence, uniqueness.
Mathematics Subject Classification: 26A33, 34B05.
- Received: 2010-12-10.
- Revised: 2011-01-17.
- Accepted: 2011-01-31.