Stability analysis of conformable fractional-order nonlinear systems depending on a parameter

Abstract

In this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.

Partial Stability of Conformable Stochastic Systems

“…In particular, the asymptotic behaviour and the stability theory of the solution of ordinary stochastic systems, conformable fractional-order stochastic systems, and deterministic systems were investigated by many researchers (see [2][3][4][5][6]).…”

“…In the last decades, it has established its effectiveness as an essential tool in many real-world applications, such as physics [7], biology [4,8,9], and control theory [2,3,5,[10][11][12][13][14]. In fact, Neirameh in [4] proposed a new method to find exact solutions of the general biological population model.…”

“…In the last years, the stability analysis of conformable systems was investigated by many researchers. In [2,3,12], the authors studied the stability of the solution of conformable deterministic systems. In the literature, there is a few work about the stability of the solution of conformable stochastic systems (see [5,6]).…”

Controllability of Differential Systems with the General Conformable Derivative

“…Recently, Abdeljawad [10] worked to improve such a derivative. Much research and descriptions are currently being carried out on it, and we give the following related works [11,12]. Indeed, authors in [11] worked on the analytical solutions of the system of conformable time-fractional Robertson equations with 1D diffusion.…”

“…Indeed, authors in [11] worked on the analytical solutions of the system of conformable time-fractional Robertson equations with 1D diffusion. Furthermore, authors in [12] detailed the stability analysis of conformable fractional-order nonlinear systems depending on a parameter. After that, a generalization of the classical conformable fractional derivative is investigated [13,14].…”