Stability analysis of linear conformable fractional differential equations system with time delays

Mohammadnezhad, Vahid; Eslami, Mostafa; Rezazadeh, Hadi

doi:10.5269/bspm.v38i6.37010

Cited by 26 publications

(21 citation statements)

References 22 publications

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“…As shown in Section 3, our results agree with Mohammadnezhad's conformable Euler's method [75]. Using our proposed discretization scheme, we will detect the hyperchaotic attractor of a fivedimensional fractional-order financial system.…”

Section: Introductionsupporting

confidence: 82%

“…Section 2 presents a conformable derivative hyperchaotic financial system with market confidence and ethics risk. Section 3 provides a conceptual overview of conformable calculus and propose a conformable discretezation process, which coincides with Mohammadnezhad's conformable Euler's method [75]. In section 4, we detect the hyperchaotic attractor from the proposed financial system.…”

Section: Introductionmentioning

confidence: 99%

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Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

et al. 2019

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A new chaotic financial system is proposed by considering ethics involvement in a fourdimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integerorder system. A discretization scheme is proposed to calculate numerical solutions of conformable derivative systems. The scheme is illustrated by testing hyperchaos for the system. among interest rates, investments, prices, and savings. Chen [12] presented a fractional form of nonlinear financial system. Wang, Huang and Shen [13] established an uncertain fractional-order form of the financial system. Mircea et al. [14] set up a delayed form of the financial system. Xin, Chen, and Ma [15] proposed a discrete form of financial system. Yu, Cai, and Li [16] extended the

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Section: Introductionsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

et al. 2019

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“…For more details on stability, we refer to [11,12,[21][22][23][24][25]. Stability of equilibrium points for φ t in F(R n ) is characterized by the following result.…”

Section: Preliminariesmentioning

confidence: 99%

Stability of Fuzzy Dynamical Systems via Lyapunov Functions

Allaoui

Melliani

Chadli

2020

International Journal of Differential Equations

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The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.

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“…Since then, the theory of conformable fractional calculus and its applications have been studied by many authors (see, for instance, [9][10][11][12][13][14][15]). Chung [16] used the conformable fractional derivative and integral to discuss fractional Newtonian mechanics and Rezazadeh et al [17] investigated the stability of linear conformable fractional systems from the point view of control theory (see also [18]). It is worth noting that the conformable fractional derivative does not have a physical meaning as the Riemann-Liouville or Caputo derivatives.…”

Section: Introductionmentioning

confidence: 99%

A new conformable nabla derivative and its application on arbitrary time scales

Rahmat

Noorani

2021

Adv Differ Equ

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In this article, we introduce a new type of conformable derivative and integral which involve the time scale power function $\widehat{\mathcal{G}}_{\eta }(t, a)$ G ˆ η ( t , a ) for $t,a\in \mathbb{T}$ t , a ∈ T . The time scale power function takes the form $(t-a)^{\eta }$ ( t − a ) η for $\mathbb{T}=\mathbb{R}$ T = R which reduces to the definition of conformable fractional derivative defined by Khalil et al. (2014). For the discrete time scales, it is completely novel, where the power function takes the form $(t-a)^{(\eta )}$ ( t − a ) ( η ) which is an increasing factorial function suitable for discrete time scales analysis. We introduce a new conformable exponential function and study its properties. Finally, we consider the conformable dynamic equation of the form $\bigtriangledown _{a}^{\gamma }y(t)=y(t, f(t))$ ▽ a γ y ( t ) = y ( t , f ( t ) ) , and study the existence and uniqueness of the solution. As an application, we show that the conformable exponential function is the unique solution to the given dynamic equation. We also examine the analogue of Gronwall’s inequality and its application on time scales.

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Stability analysis of linear conformable fractional differential equations system with time delays

Cited by 26 publications

References 22 publications

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

Stability of Fuzzy Dynamical Systems via Lyapunov Functions

A new conformable nabla derivative and its application on arbitrary time scales

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