Results on the Approximate Controllability of Hilfer Type fractional Semilinear Control Systems

The approximate controllability of Hilfer fractional semilinear control systems is the main focus of this study. Two distinct kinds of necessary requirements have been investigated. For the first set of results, we use Schauder's fixed point techniques, compactness of the relevant fractional operator, and concepts on fractional derivative to obtain them. Utilizing the Gronwall's inequality in the second set, we are able to demonstrate the main points without using the corresponding fractional operator's compactness or the fixed point method. Also provided is a case study for the validation of theoretical findings.