On controllability for a nondensely defined fractional differential equation with a deviated argument

This article deals with a fractional differential equation with a deviated argument defined on a nondense set. A fixed-point theorem and the concept of measure of noncompactness are used to prove the existence of a mild solution. Furthermore, by using the compactness of associated cosine family, we proved that system is approximately controllable and obtains an optimal control which minimizes the performance index. To illustrate the abstract result, we included an example.

Exact and trajectory controllability of second order nonlinear differential equations with deviated argument

In this manuscript, we consider a control system governed by a second order nonlinear differential equations with deviated argument in a Hilbert space X. We used the strongly continuous cosine family of bounded linear operators and fixed point method to study the exact and trajectory controllability. Also, we study the exact controllability of the nonlocal control problem. Finally, we give an example to illustrate the application of these results.