The applicability of the generalized thermoelastic theories with integer-order derivative in solving anomalous or transient thermoelastic diffusion problems is questionable. Due to the feature of memory-dependence and heredity, the fractional-order derivative and the memory-dependent derivative are introduced to modify the generalized thermoelastic theories for extending their applicability. To demonstrate the features of such theories, the thermoelastic-diffusive dynamic response of an infinite elastic medium containing a spherical cavity with variable material properties is investigated in three different generalized theories with memory-dependent effect, which are incorporated in a unified form. Of them, two are based on fractional-order derivative and the other one is based on the memory-dependent derivative. The corresponding governing equations are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress, concentration and chemical potential under the three theories are obtained and illustrated graphically for comparing with those obtained from one of the integer-order theories. The effects of the fractional-order parameter, the time-delay factor, the variable thermal conductivity and diffusivity on the variations of the considered variables are considered and discussed in detail.

具有整数阶导数的广义热弹性理论在解决异常或瞬态热弹性扩散问题中的适用性值得怀疑。由于记忆依赖和遗传的特点，引入分数阶导数和记忆依赖导数对广义热弹性理论进行修正，以扩展其适用性。为了证明这些理论的特征，包含具有可变材料特性的球形腔的无限弹性介质的热弹性 - 扩散动态响应在三种不同的具有记忆相关效应的广义理论中进行了研究，这些理论以统一的形式结合起来。其中，两种基于分数阶导数，另一种基于记忆相关导数。制定相应的控制方程，然后通过拉普拉斯变换及其数值反演求解。得到了三种理论下的无量纲温度、位移、应力、浓度和化学势的分布，并以图形方式说明，以便与从整数阶理论中获得的那些进行比较。分数阶参数、时间延迟因子、可变热导率和扩散率对所考虑变量的变化的影响进行了详细的考虑和讨论。获得了三种理论下的浓度和化学势，并以图形方式说明，以便与从整数阶理论之一获得的结果进行比较。分数阶参数、时间延迟因子、可变热导率和扩散率对所考虑变量的变化的影响进行了详细的考虑和讨论。获得了三种理论下的浓度和化学势，并以图形方式说明，以便与从整数阶理论之一获得的结果进行比较。分数阶参数、时间延迟因子、可变热导率和扩散率对所考虑变量的变化的影响进行了详细的考虑和讨论。