Exact controllability of semilinear control systems involving conformable fractional derivatives

Jneid, Maher

doi:10.1063/1.5127482

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…They significantly contribute in the analysis and design of control systems [17]. Recently, numerous researchers have investigated generalizing the fundamental controllability principles to the domain of fractional-order control systems, see [18][19][20], and the references cited therein.…”

Section: θ(T)mentioning

confidence: 99%

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Awadalla,

Chaouk,

Jneid

et al. 2024

Fractal Fract

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In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We show that the controllability of the local fractional system can be determined by the invertibility of the Gramian matrix and the full rank of the Kalman matrix. We also show that the local fractional system involving distinct orders is controllable if and only if the Gramian matrix is invertible. Illustrative examples and an application are provided to demonstrate the validity of the theoretical findings.

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Section: θ(T)mentioning

confidence: 99%

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Awadalla,

Chaouk,

Jneid

et al. 2024

Fractal Fract

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“…Te majority of previous researches concerning controllability issues of fractional control systems have employed the Riemann-Liouville, Caputo, and Hilfer fractional derivatives. Nevertheless, there has been limited investigation into the controllability problems associated with fractional systems using the conformable fractional derivative [25][26][27][28]. Tis represents a notable gap in the existing body of literature, considering that the conformable fractional derivative ofers several advantages compared to the Riemann-Liouville, Caputo and Hilfer fractional derivatives, including its greater naturalness and geometric intuitiveness.…”

Section: Introductionmentioning

confidence: 99%

On Partial Exact Controllability of Fractional Control Systems in Conformable Sense

Jneid

2024

Journal of Mathematics

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In this work, we investigate the partial exact controllability of fractional semilinear control systems in the sense of conformable derivatives. Initially, we establish the existence and uniqueness of the mild solution for this type of fractional control systems. Then, by employing a contraction mapping principle, we obtain sufficient conditions for the conformable fractional semilinear system to be partially exactly controllable, assuming that its associated linear part is partially exactly controllable. To demonstrate the efficacy of the theoretical findings, a typical example is provided at the end.

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“…Recently, the study of control problems has attracted the attention of many mathematicians and physicists in various fields of science [44][45][46][47][48][49][50]. For example, in theory of differential equations, the controllability consists to control evolution systems from the initial position to the desired position.…”

Section: Introductionmentioning

confidence: 99%

Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations

Hannabou

Bouaouid

Hilal

2022

Advances in Mathematical Physics

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In many research works Bouaouid et al. have proved the existence of mild solutions of an abstract class of nonlocal conformable fractional Cauchy problem of the form: d α x t / d t α = A x t + f t , x t , x 0 = x 0 + g x , t ∈ 0 , τ . The present paper is a continuation of these works in order to study the controllability of mild solution of the above Cauchy problem. Precisely, we shall be concerned with the controllability of mild solution of the following Cauchy problem d α x t / d t α = A x t + f t , x t + B u t , x 0 = x 0 + g x , t ∈ 0 , τ , where d α . / d t α is the vectorial conformable fractional derivative of order α ∈ 0 , 1 in a Banach space X and A is the infinitesimal generator of a semigroup T t t ≥ 0 on X . The element x 0 is a fixed vector in X and f , g are given functions. The control function u is an element of L 2 0 , τ , U with U is a Banach space and B is a bounded linear operator from U into X .

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Exact controllability of semilinear control systems involving conformable fractional derivatives

Cited by 8 publications

References 10 publications

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

Processing the Controllability of Control Systems with Distinct Fractional Derivatives via Kalman Filter and Gramian Matrix

On Partial Exact Controllability of Fractional Control Systems in Conformable Sense

Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations

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