  Our general aim is to give sufficient conditions for robustness behavior and
convergence to the equilibrium point of linear time-varying fractional system's
solutions. We approach this problem using as a framework a series of recent
results due to Cong et al. We establish theorems that generalize in several
ways many previous results in the specialized literature, including those of
Cong et al. We use the proposed theorems in adaptive systems, proving
convergence and robustness of such schemes, that up to date remain unsolved
problems, showing the wide scope of application of our results.
