Boundary value problems for impulsive Bagley–Torvik models involving the Riemann–Liouville fractional derivatives

By using the Picard iterative technique, we get the exact expression of solutions of linear fractional Bagley–Torvik model. Then the piecewise continuous solutions of this kind of models are obtained. By using these results, we convert the boundary value problems for impulsive fractional differential equations to integral equations technically. By using the weighted function Banach spaces, the completely continuous operators and the Schauder’s fixed point theorem, some existence results for solutions of the boundary value problems for impulsive Bagley–Torvik fractional differential equations are established. Examples are given to illustrate the main results. © 2016, Instituto de Matemática e Estatística da Universidade de São Paulo.