Fractional order thermoelastic wave assessment in a two-dimension medium with voids

Aatef D. Hobiny , Ibrahim A. Abbas

Abstract

In this article, the generalized thermoelastic theory with fractional derivative is presented to estimate the variation of temperature, the components of stress, the components of displacement and the changes in volume fraction field in two-dimensional porous media. Easily, the exact solutions in the Laplace domain are obtained. By using Laplace and Fourier transformations with the eigenvalues method, the physical quantities are obtained analytically. The numerical results for all the physical quantities considered are implemented and presented graphically. The results display that the present model with the fractional derivative is reduced to the Lord and Shulman (LS) and the classical dynamical coupled (CT) theories when the fractional parameter is equivalent to one and the delay time is equal to zero and respectively.

Key Words

fractional derivative; Laplace-Fourier transforms; porous medium; eigenvalues approach

Address

Aatef D. Hobiny — Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
Ibrahim A. Abbas — 1.) Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia 2.) Department of mathematics, Faculty of Science, Sohag University, Sohag, Egypt

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