Approximate controllability analysis on nonlinear fractional evolution equations

This paper aims to study the approximate controllability for a class of nonlinear fractional evolution systems with Hadamard-Caputo fractional derivatives. By investigating the compactness of the solution operator and by utilizing the Schauder's fixed-point theorem, the existence of the mild solution for the considered system is provided. Based on these, the approximate controllability result is derived. Finally, an example is given to show the correctness of our results.