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Asymptotic Properties of General Nonlinear Differential Equations Containing Nonconformable Fractional Derivatives

Graef John R.

Journal of Mathematics and Applications

2024

Vol. 47

23--37

In this paper the author employs the nonconformable fractional derivative developed by J. E. N´apoles Valdes and his coauthors to study the asymptotic properties of solutions of a broad class of nonlinear fractional differential equations containing such a type of derivative. Sufficient conditions for the boundedness and convergence to zero of all solutions are presented.

Exponential stability of non-conformable fractional-order systems

Echi Nadhem, Mabrouk Fehmi, Omri Faouzi

Journal of Applied Analysis

2024

Vol. 30, nr 2

407--415

Recently, the authors Guzman et al. (2018) introduced a new simple well-behaved definition of the fractional derivative called non-conformable fractional derivative. In this paper we study the exponential stability of non-conformable fractional-order systems by using the Lyapunov function and Gronwall inequality. These inequalities can be used as handy tools to research stability problems of nonlinear systems. Sufficient conditions for exponential stability are given using the Lyapunov theory. Further, deals with the state feedback stabilization problems for a family of nonlinear systems satisfying a Lipschitz continuity condition. The stability of the controller is proved by means of the new Lyapunov stability theorem given in this paper. A numerical example is given to illustrate the efficiency of the obtained result.