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Journal of Mathematics
Volume 2013, Article ID 489863, 11 pages
http://dx.doi.org/10.1155/2013/489863
Research Article

The Effect of Magnetic Field and Initial Stress on Fractional Order Generalized Thermoelastic Half-Space

Department of Mathematics, G. J. University of Science and Technology, Haryana, Hisar 125001, India

Received 26 December 2012; Revised 5 March 2013; Accepted 12 March 2013

Academic Editor: Petr Ekel

Copyright © 2013 Sunita Deswal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.