Approximate controllability of nonlinear fractional dynamical systems

作者：Sakthivel, R.^*; Ganesh, R.; Ren, Yong; Anthoni, S. M.

来源：Communications in Nonlinear Science & Numerical Simulation, 2013, 18(12): 3498-3508.

DOI：10.1016/j.cnsns.2013.05.015

• Approximate controllability
• Fractional differential equations
• Nonlocal conditions

In this paper, we consider the controllability problems for a class of nonlinear fractional differential equations of order 1 < q < 2 with nonlocal conditions. In particular, a set of sufficient conditions are derived for the approximate controllability of nonlinear fractional dynamical systems by assuming the associated linear system is approximately controllable. Further, the result is extended to study the approximate controllability result for the nonlocal fractional control system with infinite delay. Also, as a remark, the conditions for the exact controllability results are obtained. The results are established by using solution operator theory, fractional calculations and fixed point techniques. Finally, an example is provided to illustrate the obtained theory.

• 出版日期2013-12
• 单位安徽师范大学