Stability Analysis for Fractional-like Linear Systems

In this paper, several new definitions of fractional derivative and fractional integral for a continuous function are presented. It is shown that several results obtained are close resemblance to those found in classical calculus. A new fractional Laplace transforms are investigated as well. Based on the definitions presented, for the fractional-like linear differential system, we derive the explicit solution with the help of the fractional-like Laplace transforms. In addition, we investigate the Lyapunov stability and asymptotical stability for the fractional-like linear differential system. The conditions of stability are proposed and proven with inspiration via the traditional stability analysis. Examples illustrate the theoretical results proved in this manuscript.