A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

Pandey, Ritika; Shukla, Chandan; Shukla, Anurag; Upadhyay, Ashwini Kumar; Singh, Arun Kumar

doi:10.11121/ijocta.2023.1256

Cited by 4 publications

(1 citation statement)

References 34 publications

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“…Recently, FC started to penetrate the domain of control theory [10,13,14]; in particular, it is used to investigate the notion of regional observability; see [15][16][17][18] for linear fractional systems and [19,20] for semilinear ones. In this paper, we investigate the notion of regional boundary observability, which is basically regional observability where the desired subregion is a part of the boundary of the evolution domain [21,22].…”

Section: Introductionmentioning

confidence: 99%

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

Zguaid

Alaoui

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This paper considers the regional boundary observability problem for semilinear time-fractional systems. The main objective is to reconstruct the initial state on a subregion of the boundary of the evolution domain of the considered fractional system using the output equation. We proceed by providing a link between the regional boundary observability of the considered semilinear system on the desired boundary subregion, and the regional observability of its linear part, in a well chosen subregion of the evolution domain. By adding some assumptions on the nonlinear term appearing in the considered system, we give the main theorem that allows us to reconstruct the initial state in the well-chosen subregion using the Hilbert uniqueness method (HUM). From it, we recover the initial state on the boundary subregion. Finally, we provide a numerical example that backs up the theoretical results presented in this paper with a satisfying reconstruction error.

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Section: Introductionmentioning

confidence: 99%

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

Zguaid

Alaoui

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

Pradeesh,

Vijayakumar

2024

Qual. Theory Dyn. Syst.

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Sobolev-Type Nonlinear (k,ψ)−Hilfer Fractional Differential Equations With Control: Approximate Controllability Exploration

Mourad,

Ichrak,

Sami

2024

Journal of Computational and Nonlinear Dynamics

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This paper is concerned with the approximate controllability of Sobolev type (k, ψ) - Hilfer fractional differential equations with control and Sobolev type (k,ψ) - Hilfer fractional initial conditions in Hilbert spaces. By mean of two operators kSψα,β, kTψα and k-Probability density function, the definition of mild solutions for studied problem was given. Then, via (k, ψ) - Hilfer fractional derivative and combining the techniques of fractional calculus and fixed point theorem, we analyzed the existence and uniqueness of mild solutions. With help of Cauchy sequence and approximate techniques, we estabilish some sufficient conditions for the approximate controllability of the proposed control system. Finally, an example is presented for the demonstration of obtained results.

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A new approach on approximate controllability of Sobolev-type Hilfer fractional differential equations

Cited by 4 publications

References 34 publications

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

Sobolev-Type Nonlinear (k,ψ)−Hilfer Fractional Differential Equations With Control: Approximate Controllability Exploration

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