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Asymptotic behavior of a viscoelastic wave equation with a delay in internal fractional feedback

Aounallah Radhouane, Choucha Abdelbaki, Boulaaras Salah, Zarai Abderrahmane

Archives of Control Sciences

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2024

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Vol. 34, No. 2

379--413

EN

We consider the viscoelastic wave equation with a time delay term in internal fractional feedback. By employing the energy method along with the Faedo-Galerkin procedure, we establish the global existence of solutions, subject to certain conditions. Additionally, we demonstrate how appropriate Lyapunov functionals can lead to general decay results of the energy.

2

Source term model for elasticity system with nonlinear dissipative term in a thin domain

Dilmi Mohamed, Dilmi Mourad, Boulaaras Salah, Benseridi Hamid

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

437--451

EN

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u∗ is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

3

A robust study of the transmission dynamics of zoonotic infection through non-integer derivative

Jan Rashid, Alharbi Asma, Boulaaras Salah, Alyobi Sultan, Khan Zaryab

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

922--938

EN

In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter R0 was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.

4

Existence of positive solutions of a new class of nonlocal p(x)-Kirchhoff parabolic systems via sub-super-solutions concept

Zediri Sounia, Guefaifia Rafik, Boulaaras Salah

Journal of Applied Analysis

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2020

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Vol. 26, nr 1

49--58

EN

Motivated by the idea which has been introduced by Boulaaras and Guefaifia [S. Boulaaras and R. Guefaifia, Existence of positiveweak solutions for a class of Kirchhoff elliptic systems with multiple parameters, Math. Methods Appl. Sci. 41 (2018), no. 13, 5203-5210] and by Afrouzi and Shakeri [G. A. Afrouzi, S. Shakeri and N. T. Chung, Existence of positive solutions for variable exponent elliptic systems with multiple parameters, Afr. Mat. 26 (2015), no. 1-2, 159-168] combined with some properties of Kirchhoff-type operators, we prove the existence of positive solutions for a new class of nonlocal p(x)-Kirchhoff parabolic systems by using the sub- and super-solutions concept.