Representation of solutions of linear conformable delay differential equations

Xiao, Guanli; Wang, JinRong

doi:10.1016/j.aml.2021.107088

Cited by 16 publications

(10 citation statements)

References 9 publications

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“…In this paper, we consider the Gauss hypergeometric function as a control function and use this function to investigate the stability of Gauss hypergeometric. In this section, we present the definitions of the fractional integral, the Riemann-Liouville fractional derivative, and the Caputo fractional derivative of order τ, which we utilize in this paper, for more detail, we refer to [11][12][13][14]. In the continuation, by introducing the Gauss hypergeometric series, we define the Gauss hypergeometric stability of equation ( 1) [15][16][17].…”

Section: Preliminariesmentioning

confidence: 99%

Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

Eidinejad

Saadati

Sen

2021

Mathematical Problems in Engineering

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In this paper, we consider a class of fractional-order differential equations and investigate two aspects of these equations. First, we consider the existence of a unique solution, and then, using a new class of control functions, we investigate the Gauss hypergeometric stability. We use Chebyshev and Bielecki norms in order to prove these aspects by the Picard method. Finally, we give some examples to illustrate our results.

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Section: Preliminariesmentioning

confidence: 99%

Picard Method for Existence, Uniqueness, and Gauss Hypergeomatric Stability of the Fractional-Order Differential Equations

Eidinejad

Saadati

Sen

2021

Mathematical Problems in Engineering

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“…This pioneering research yielded plenty of novel results on the representation of solutions, which are applied in the stability analysis and control problems of time-delay systems; see for example [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references therein. Thereafter, in 2021, Xiao et al [29] obtained the exact solutions of linear conformable fractional delay differential equations of order α ∈ (0, 1] by constructing a new conformable delayed exponential matrix function.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

Elshenhab¹,

Wang²,

Mofarreh³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayed matrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results.

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“…The conformable fractional differential operator has been introduced first in [22]. Next, the conformable fractional differential equations has been rapidly developed; see [6,7,10,11,17,18,20,21,27,28], and the reference therein.…”

Section: Introductionmentioning

confidence: 99%