Partial Approximate Controllability of a Three-Parameter Damped Fractional Diffusion Control System with Nonlinear Perturbations

In this paper, we investigate the partial approximate controllability of a class of fractional diffusion control systems with three-parameter damping and nonlinear perturbations. First, based on the theory of (μ,ν,ξ,e,k)-resolvent families developed in our previous work, we define the mild solution of the system. Then, by constructing a proper objective functional and using the strict convexity, we prove the existence and uniqueness of the minimal norm control. Furthermore, employing the Arzelà–Ascoli theorem and variational inequalities, we establish the precompactness of the solution family and derive the key controllability estimate. Finally, we provide an example to illustrate the effectiveness of our theoretical results.