The aim of the present investigation is to examine the memory-dependent derivatives (MDD) in 2D transversely isotropic homogeneous magneto thermoelastic medium with two temperatures. The problem is solved using Laplace transforms and Fourier transform technique. In order to estimate the nature of the displacements, stresses and temperature distributions in the physical domain, an efficient approximate numerical inverse Fourier and Laplace transform technique is adopted. The distribution of displacements, temperature and stresses in the homogeneous medium in the context of generalized thermoelasticity using LS (Lord-Shulman) theory is discussed and obtained in analytical form. The effect of memory-dependent derivatives is represented graphically.

中文翻译：

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具有两个温度的磁热弹性横向各向同性介质的记忆相关导数方法

本研究的目的是研究具有两个温度的二维横向各向同性均质磁热弹性介质中的记忆依赖导数（MDD）。使用拉普拉斯变换和傅立叶变换技术解决了该问题。为了估计物理域中位移，应力和温度分布的性质，采用了一种有效的近似数值傅里叶逆和拉普拉斯逆变换技术。利用LS（Lord-Shulman）理论，在广义热弹性的背景下，讨论并获得了均质介质中位移，温度和应力的分布。依赖于记忆的导数的效果以图形方式表示。