ibrabbas7

Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.

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Publications Which contain the keyword: fractional order theory


The effect of fractional derivative on photo-thermoelastic interaction in an infinite semiconducting medium with a cylindrical hole
In the present paper, the theory of generalized photo-thermoelasticity under fractional order derivative was used to study the coupled of thermal, plasma, and elastic waves on unbounded semiconductor medium with a cylindrical hole during the photo-thermoelastic process. The bounding surface of the cavity was traction free and loaded thermally by exponentially decaying pulse boundary heat flux. The medium was considered ... Read more

2018-10-14 10:06:36 Keywords fractional order theory, thermal loading, Thermoelasticity,
A study on fractional order theory in thermoelastic half-space under thermal loading
In this study, the effect of fractional order derivative on a two-dimensional problem due to thermal shock with weak, normal and strong conductivity is established. The governing equations are taken in the context of Green and Naghdi of type III model (GNIII model) under fractional order derivative. Based on the Laplace and exponential Fourier transformations with eigenvalues approach, the analytical ... 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

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

Fractional order photo-thermo-elastic waves in a two-dimensional semiconductor plate
This paper is devoted to the investigation of fractional order photo-thermo-elastic waves in a two-dimensional semiconductor using the eigenvalues approach. The formulations applied are based on the fractional order generalized thermo-elasticity in the context of the new model of heat conduction. The bounding surface of the plate is taken to be stress-free and exposed to a heat flux with the ... Read more

Fractional Order Generalized Thermoelasticity in an Unbounded Medium with Cylindrical Cavity
This paper is concerned with the investigation of the temperature, displacement, and stresses due to thermal shock loading on the inner surface cavity in an infinite medium with a cylindrical cavity. The governing equations will be taken into the context of the fractional order generalized thermoelasticity theory. In the Laplace transform domain, the form of a vector-matrix differential equation has ... Read more

Analytical Solution of Thermoelastic Damping in a Nanoscale Beam using the Fractional Order Theory of Thermoelasticity
In this paper, we study the generalized thermoelastic vibration of a bounded nano-beam resonator under fractional order theory of thermoelasticity. The theory of generalized thermoelasticity with one relaxation time can be established in the limit as the special cases of the present model. The effect of fractional parameter is investigated on the nano-beam resonator for beams with clamped ends. Analytical ... Read more

2018-10-02 21:16:19 Keywords fractional order theory, Thermoelastic Diffusion,
A Half-Space Problem in the Fractional Order Theory of Thermoelastic Diffusion
In this work, a general solution to the field equations of generalized thermoelastic diffusion in a half-space is considered in the context of fractional order theory of thermoelastic diffusion. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock while the chemical potential is assumed to be a known function ... Read more

Fractional Order Theory of Thermoelastic Diffusion Problem for an Infinite Medium with Cylindrical Cavity
The fractional order theory of generalized thermoelastic diffusion with relaxation times, in the context of Lord and Shulman theory, is used to investigate the thermoelastic diffusion problem in an infinite medium with a cylindrical cavity. The surface of cavity is taken to be traction free and subjected to heating. The chemical potential is assumed a known function of time on ... Read more

Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity
In this work, we study a problem in a fractional order theory of thermoelastic diffusion in an infinite medium with a spherical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity. The chemical potential is assumed a known function of time on the bounding cavity. The form of vector–matrix differential ... Read more