Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
766934 | Communications in Nonlinear Science and Numerical Simulation | 2013 | 14 Pages |
In this paper, a generalized anti-periodic boundary value problem for an impulsive fractional differential equation is studied. A natural formula of solutions is derived and new existence theorems of the solutions are established under the mixed nonlinear DD-contraction condition, comparison condition, sublinear growth condition and nonlinear growth condition via fixed point methods. In particular, a new special hybrid singular type Gronwall inequality is established to obtain a prior bounds of the solutions.
► A generalized anti-periodic boundary value problem for an impulsive fractional differential equation is studied. ► A natural formula of solutions is derived and new existence theorems of the solutions are established. ► A new special hybrid singular type Gronwall inequality is established.