A discussion on controllability of nonlocal fractional semilinear equations of order 1<r<2 with monotonic nonlinearity

In this article, we use the tool of monotone nonlinearity to present the approximate controllability discussion for fractional semilinear system with nonlocal conditions. Monotonicity is an important characteristic in many communications applications in which digital-to-analog converter circuits are used. Such applications can function in the presence of nonlinearity, but not in the presence of non-monotonicity. Therefore, it becomes quite interesting to study a problem assuming monotonicity of the nonlinear function. Also, nonlocal conditions are additional specifications for the physical measurements than classical ones and impart a finer effect on the solution. We formulate the control function for the problem and establish the controllability results. At last, we proposed two applications for the demonstration.