Yang, Jun; Liu, Dongli; Zhang, Bo Existence of solutions for higher-order impulsive boundary value problems of a quasilinear fractional differential equation. (Chinese. English summary) Zbl 1313.34028 Acta Sci. Nat. Univ. Sunyatseni 53, No. 1, 34-41 (2014). Summary: The existence of solutions for higher-order impulsive boundary value problems of the form \[ \begin{aligned} & D^q_{0+}y(t)=A(t,y)y(t)+f(t,y(t),\varPhi y(t),\varPsi y(t)) \forall t\in [0,1], q\in (n-1,n],\\ & y^{(i)}(0)=0,\Delta y^{(i)}|_{t=t_k}=0, 1\leqslant i\leqslant n-2, k=1,2,\cdots, p,\\ & \Delta y|_{t=t_k}=I_k(y(t_k)),\Delta y^{(n-1)}|_{t=t_k}=J_k(y(t_k)), k=1,2,\cdots, p,\\ & y(0)=y_0+g(y),\;y^{(n-1)}(1)=y_1+\sum\limits^{m-2}_{j=1}b_jy^{(n-1)}(\xi_j)\end{aligned} \] is studied. By defining a contraction mapping and using a fixed point theorem, some sufficient conditions for the existence of a unique solution and at least one solution are established. Furthermore, two examples are presented to illustrate the main results. Cited in 1 Document MSC: 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B37 Boundary value problems with impulses for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:fractional differential equations; Caputo fractional derivative; fixed-point theorems PDFBibTeX XMLCite \textit{J. Yang} et al., Acta Sci. Nat. Univ. Sunyatseni 53, No. 1, 34--41 (2014; Zbl 1313.34028)