Investigation of controllability and stability of fractional dynamical systems with delay in control

Selvam, Anjapuli Panneer; Govindaraj, Venkatesan

doi:10.1016/j.matcom.2024.01.011

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…According to (11) and ( 12), a nonlinear system of algebraic type is obtained, and by solving it, solutions of (12) are obtained.…”

Section: The First Kudryashov-type Methodsmentioning

confidence: 99%

“…Stability in the Ulam sense is important since it introduces analytical approximate solutions for diverse problems where exact solutions are difficult to obtain. If a system is Ulam stable, then essential properties hold in the vicinity of the exact solution (see [11][12][13] and their references) and this is seen in optimization, biology and economics (especially when very little is known in regards to exact solutions). Ulam-type stability was first proposed in Ulam's talk at a conference in 1940 [14], and he phrased it as follows: Let M be a group and N a metric group with metric d. Given ε > 0, is there a δ > 0, such that if a mapping g : M → N satisfies d(g(yx), g(y)g(x)) ≤ δ, for every y, x ∈ M, then, there exists a homomorphism h : M → N with d(g(x), h(x)) ≤ ε, for all x ∈ M?…”

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Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Aderyani,

Saadati,

O’Regan

et al. 2024

Mathematics

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We apply known special functions from the literature (and these include the Fox H–function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the G–function, the Fox–Wright function and the Meijer G–function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory.

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“…According to (11) and ( 12), a nonlinear system of algebraic type is obtained, and by solving it, solutions of (12) are obtained.…”

Section: The First Kudryashov-type Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Aderyani,

Saadati,

O’Regan

et al. 2024

Mathematics

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Chaos and attraction domain of fractional Φ6‐van der Pol with time delay velocity

Xie,

Shi

et al. 2024

Math Methods in App Sciences

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This article investigates the chaotic analysis and attractive domain of a fractional‐order ‐van der Pol with time delay velocity under harmonic excitation. Firstly, eight different types of bifurcation states of the system under different parameters are calculated by using the undisturbed system. Secondly, the Melnikov method is used to explore the effect of time delay velocity on the threshold of chaos in the Smale horseshoe sense under the double‐well potential and three‐well potential of the system. Finally, through numerical analysis of the phase diagram, bifurcation diagram, and maximum Lyapunov exponent, the influence of time delay velocity on system chaos is studied. The results indicate that an increase in the delay velocity coefficient will lead to the system transitioning from a chaotic state to a periodic state, while an increase in the delay velocity term will lead to the system transitioning from a periodic state to a chaotic state. In the study of system bifurcation, it is found that the position of the equilibrium points of the system changes during periodic motion. Therefore, cell mapping is used to draw the attractive domain of the system is studying the influence of initial conditions on the equilibrium point of the system and the results show that there is a close relationship between the attraction domain and the process of chaos occurrence.

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Qualitative analysis and modulation instability for the extended (3+1)-dimensional nonlinear Schrödinger equation with conformable derivative

Zhang,

Li,

Cao

2024

Results in Physics

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Investigation of controllability and stability of fractional dynamical systems with delay in control

Cited by 3 publications

References 28 publications

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Chaos and attraction domain of fractional Φ6‐van der Pol with time delay velocity

Qualitative analysis and modulation instability for the extended (3+1)-dimensional nonlinear Schrödinger equation with conformable derivative

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