Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.


A DPL model of photothermal interaction in a semiconductor material
The generalized model for plasma, thermal, and elastic waves under dual phase lag model have been applied to determine the carrier density, the displacement, the temperature, and the stresses in a semiconductor medium. Using Laplace transform and the eigenvalue approach methodology, the solutions of all variables have been obtained analytically. A semiconducting material like as silicon was considered. The results ... Read more

2019 | Keywords
Solutions of Some Difference Equations Systems and Periodicity
In this article, analysis and investigation have been conducted on the periodic nature as well as the type of the solutions of the subsequent schemes of rational difference equations Read more

Eigenvalue approach for generalized thermoelastic porous medium under the effect of thermal loading due to a laser pulse in DPL model
The aim of the present study is concerned with the thermal loading due to laser pulse on thermoelastic porous medium under dual-phase-lag model DPL. The material is a homogeneous isotropic elastic half-space and heated by a non-Gaussian laser beam with the pulse duration of 8 ps. Eigenvalue approach is proposed to analyze the problem and obtain the analytical solutions of ... Read more

An analytical study on the fractional transient heating within the skin tissue during the thermal therapy
In the present paper, the bioheat equation under fractional derivatives is used to study the thermal damage within the skin tissue during the thermal therapy. Basically, the analytical solutions in the Laplace domain are easily obtainable. The influences of the fractional derivative and moving heat source velocity on the temperature of skin tissues and the thermal injuries are precisely investigated. ... Read more

Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material
In the present paper, the wave propagation on non-homogenous semiconductor through photo-thermal process has been studied by using the theory of coupled plasma and thermoelastic wave. Without neglecting the coupling between the plasma and thermoelastic wave that photo-generated through intensity modulated laser beam and tightly focused, a semiconducting isotropic elastic medium has non-homogeneity in thermal and elastic properties are considered. ... Read more

Fractional order theory in a semiconductor medium photogenerated by a focused laser beam
In this paper, the fractional order theory has been applied for thermal, elastic and plasma waves to determine the carrier density, displacement, temperature and stress in a semiconductor medium. The thermal, elastic and plasma waves in a semi-infinite medium photogenerated by a focused laser beam were analyzed. The Laplace transformation is used to express the governing equation and solved analytically ... Read more

Analytical solution of fractional order photo-thermoelasticity in a non-homogenous semiconductor medium
The purpose of this paper is to study the wave propagation in a non-homogenous semiconducting medium through the photothermal process using the fractional order photo-thermoelastic without neglecting the coupling between the plasma and thermoelastic waves that photogenerated through traction free and loaded thermally by exponentially decaying pulse boundary heat flux. Read more

Theoretical analysis of thermal damages in skin tissue induced by intense moving heat source
In this paper, the analytical solution of hyperbolic bio-heat equation under intense moving heat source is presented. The exact solution in the domain of Laplace's transform is obtained. The thermal damages to the tissues are evaluated by the extent of the denatured protein employing with the Arrhenius equation. The results indicate that the hyperbolic bio-heat model reduces to the parabolic ... Read more

Analytical Solutions of Plasma and Thermoelastic Waves Photogenerated by a Focused Laser Beam in a Semiconductor Material
In the present work, the coupled plasma theory (thermally and elasticity waves) was used to study the wave propagation of semiconducting sample through photothermal process. The coupled of the plasma, thermally, and elastic waves that photo-generated through intensity modulated laser beam and tightly focused has been considered to study an elastic homogeneous semiconducting medium with isotropic thermo-elastic properties. Laplace transformations ... Read more

A mode I crack problem for a thermoelastic fibre-reinforced anisotropic material using finite element method
In this article, the theory of generalized thermoelasticity with one relaxation time is used to investigate the thermoelastic fiber-reinforced anisotropic material with a finite linear crack. The crack boundary is due to a prescribed temperature and stress distribution. By using the finite element method, the numerical solutions of the components of displacement, temperature and the stress components have been obtained. ... Read more