Abstract
This article studies the generalized Mittag–Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method. A new Hilfer type fractional comparison principle is also proved. The novelty of this article is the fractional Lyapunov direct method combined with the Hilfer type fractional comparison principle. Finally, our main results are explained by some examples.
Highlights
Fractional calculus, as one of the more powerful tools to deal with complex phenomena, is getting more and more attention
To the best of our knowledge, while some research has been carried on the stability of the Riemann–Liouville or Caputo fractional order systems, no single study exists which has investigated the stability of the Hilfer fractional order system by using Lyapunov direct method (LDM)
We studied the generalized Mittag–Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method
Summary
Fractional calculus, as one of the more powerful tools to deal with complex phenomena, is getting more and more attention. The Lyapunov direct method (LDM) is one of the more important methods to analyze stability of fractional order systems. To the best of our knowledge, while some research has been carried on the stability of the Riemann–Liouville or Caputo fractional order systems, no single study exists which has investigated the stability of the Hilfer fractional order system by using LDM. In this context, the dual index of the Hilfer fractional derivative is complex but fascinating.
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