Construction controllability for conformable fractional stochastic evolution system with noninstantaneous impulse and nonlocal condition

Ahmed, Hamdy M.

doi:10.1016/j.spl.2022.109618

Cited by 5 publications

(2 citation statements)

References 20 publications

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“…For future work, we can present the approximate/null controllability of instantaneous/noninstantaneous impulsive conformable stochastic evolution equations/inclusions with different stochastic perturbations, see [20][21][22].…”

Section: Discussionmentioning

confidence: 99%

“…A qualitative analysis of linear/semi-linear/non-linear deterministic/stochastic differential equations and delay differential equations with a conformable/classical derivative was studied in [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and the Caputo derivative equations were studied in [26][27][28]. The concept of conformable derivative is used in the study of nonlinear control systems, where the goal is to find a suitable control input that will steer the system from one state to another in a desired manner.…”

Section: Introductionmentioning

confidence: 99%

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A Study on Existence and Controllability of Conformable Impulsive Equations

Mahmudov

2023

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We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative approach, we introduce the conformable controllability operator and the conformable controllability Gramian matrix in order to obtain the necessary and sufficient conditions for the complete controllability of linear impulsive conformable systems. We present a set of sufficient conditions for the controllability of the conformable semilinear impulsive systems.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Study on Existence and Controllability of Conformable Impulsive Equations

Mahmudov

2023

Axioms

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Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness

Huang

Luo

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this article, we consider conformable fractional stochastic differential equations (CFSDEs) driven by fBm with infinite delay via measures of noncompactness (MNC). As far as we know, there are few papers considering this issue. First, by virtue of a Mönch fixed point theorem and MNC, we explore the existence of solutions for CFSDEs. Subsequently, with the aid of Jensen inequality, Hölder inequality, stochastic analysis techniques, and semigroup theory, the controllability for this considered CFSDEs is investigated by employing a Mönch fixed point theorem. Thereafter, the controllability of CFSDEs with nonlocal conditions is discussed. Finally, the theoretical result is supported through an example.

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Results on partial approximate controllability of fractional control systems in Hilbert spaces with conformable derivatives

Jneid

2024

AIP Advances

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This paper investigates partial approximate controllability of fractional linear and semi-linear control systems involving the conformable derivative. First, we derive sufficient and necessary conditions for partial approximate controllability of fractional linear systems over a small interval. Then, we apply a new approach, different from typical methods involving complexity inequalities and fixed point theorems, to obtain sufficient conditions for partial approximate controllability of semi-linear fractional control systems, assuming that the linear part is partially approximately controllable. The effectiveness of these results is demonstrated through an illustrative example.

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Construction controllability for conformable fractional stochastic evolution system with noninstantaneous impulse and nonlocal condition

Cited by 5 publications

References 20 publications

A Study on Existence and Controllability of Conformable Impulsive Equations

A Study on Existence and Controllability of Conformable Impulsive Equations

Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness

Results on partial approximate controllability of fractional control systems in Hilbert spaces with conformable derivatives

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