Approximate controllability and optimal controls of fractional dynamical systems of order 1 < q < 2 in Banach spaces

• DOI: 10.1186/s13662-015-0399-5
• Publication Date: 2015-03-03T03:35:54Z
• Authors: Haiyong Qin; Xin Zuo; Jianwei Liu; Lishan Liu
• Keywords: C0-semigroup

This paper investigates the approximate controllability and optimal controls of fractional dynamical systems order $1< q<2$ in Banach spaces. We research a class governed by integrodifferential equations with nonlocal initial conditions. Using Krasnosel’skii fixed point theorem Schauder theorem, results are obtained under two cases nonlinear term. also present existence pairs corresponding control Bolza cost function. Finally, an application is given to illustrate effectiveness our main results.