Existence of Solutions for Second Order Partial Neutral Functional Differential Equations

Morales, Eduardo Hernández; Henrı́quez, Hernán R.; McKibben, Mark A.

doi:10.1007/s00020-008-1618-1

Cited by 19 publications

(3 citation statements)

References 24 publications

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“…may be proved by combining the results in [6,7,19,34] and [8,18,24]. We shall assume therefore that the solution and the initial data are regular enough to justify our computation.…”

Section: Introductionmentioning

confidence: 99%

Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Kerbal¹,

Tatar²

2019

Turk J Math

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A Timoshenko type beam subject to a viscoelastic damping in the rotational displacement component is considered. Taking into account a neutral type delay, we prove a fast stability result despite the previously observed destabilizing effect due to delays in such systems. The proof relies on the introduction of nine different functionals with which we modify the energy of the system. These functionals are carefully selected and adapted to cope with both the viscoelasticity and the neutral delay.

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“…may be proved by combining the results in [6,7,19,34] and [8,18,24]. We shall assume therefore that the solution and the initial data are regular enough to justify our computation.…”

Section: Introductionmentioning

confidence: 99%

Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Kerbal¹,

Tatar²

2019

Turk J Math

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“…These models may be classified into two distinct types. The first group employs neutral functional differential equations [11], whereas the second category utilizes retarded functional differential equations [9]- [12]. Therefore, we suggest utilizing a ball and plate system model that relies on retarded functional equations [9], together with frequency domain synthesis techniques (refer to [2] and [10]), to construct a state feedback control rule [2].…”

Section: Introductionmentioning

confidence: 99%

State-Feedback Control of Ball-Plate System: Geometric Approach

Lefrouni,

Taibi

2024

IJACSA

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This research focuses on investigating the issue of accurately controlling the location of the ball in the ball and plate system. The findings of this research have practical applications across several domains, including optimizing the alignment of solar panels to enhance their energy generation capacity. In this work, we propose the development of a system dynamics model using the Euler-Lagrangian approach. Furthermore, we analyze a technique in the frequency domain known as the geometric approach to create a state-feedback control that ensures the stability of the system. This study primarily focuses on analyzing the characteristic equations associated with the closed-loop system, while also considering the impact of feedback delay. Ultimately, the proposed technique is substantiated by presenting simulation data for validation.

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“…We refer the reader to [25,26] for an introduction to the theory of the cosine family. Several results on classical solutions and mild solutions have been proved under different conditions on the nonlinearities and the initial data [4,6,7,8,9,13,14,27]. In case β = 1, the natural underlying space where to look for mild solutions is the space of continuously differentiable functions.…”

Section: Introductionmentioning

confidence: 99%

On a Second-Order Differential Problem With Fractional Derivatives of Order Greater Than One

Tatar

2013

Mathematical Modelling and Analysis

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A second-order abstract problem with derivatives of non-integer order is investigated. The nonlinearity involves fractional derivatives between 1 and 2. Existence and uniqueness of mild and classical solutions are established in appropriate spaces. This work extends similar works with or without a derivative of first order and also a work of the present author, where the order of the derivatives were between 0 and 1.

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Existence of Solutions for Second Order Partial Neutral Functional Differential Equations

Abstract: We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space. Mathematics Subject Classification (2000). Primary 35R10; Secondary 34K30, 34K40, 47D09.

Cited by 19 publications

References 24 publications

Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

Exponential stabilization of a neutrally delayed viscoelastic Timoshenko beam

State-Feedback Control of Ball-Plate System: Geometric Approach

On a Second-Order Differential Problem With Fractional Derivatives of Order Greater Than One

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