An isotropic homogeneous thermoelastic half-space has been considered with permeating gas, thermal pulse, and chemical potential on the bounding plane. A three-dimensional generalized thermo-diffusion model with three-phase lag has been constructed in the context of Memory-dependent derivative (MDD). Laplace transform (time domain) and Double Fourier transform (space domain) have been used in the formulation of the problem and thus the solutions for temperature increment, invariant stress, chemical potential and diffusion concentration are obtained using eigenvalue approach. Finally the effect of kernel function has been discussed and also the results are depicted in several dimensions.

考虑了边界平面上的渗透气体、热脉冲和化学势的各向同性均匀热弹性半空间。在记忆相关导数（MDD）的背景下构建了具有三相滞后的三维广义热扩散模型。问题的表述中使用了拉普拉斯变换（时域）和双傅里叶变换（空间域），因此使用特征值方法获得了温度增量、不变应力、化学势和扩散浓度的解。最后讨论了核函数的影响，并从多个维度描述了结果。