In the present analysis, the non-local behavior during thermal lagging is studied to accommodate the effect of the thermomass for a piezoelastic half-space due to the influence of magnetic field in the context of dual-phase-lag model of generalized thermoelasticity, defined in an integral form of a common derivative on a slipping interval. Simultaneous existence of the nonlocality (in space) and lagging (in time) behaviors give rise to a new type of thermal waves, which can be of major significance. In the current analysis, Danilovskaya's problem has been solved in which, the thermal shock is employed on the boundary of the half-space, which is traction-free. Employing the Laplace transform, the problem has been solved and the solution in the space-time domain is achieved on applying Riemann-sum approximation technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Several graphical representations are shown to analyze the effects of different parameters and to mark the variation of this non-local model with previously existing models. Excellent predictive capability is demonstrated due to the presence of magnetic filed, memory-dependent derivative, the electric displacement and time-delay parameter, and the effect of correlating length is also reported.

在本分析中，研究了热滞后期间的非局部行为，以适应在广义热弹性的双相滞后模型的背景下，由于磁场的影响，热质量对压电弹性半空间的影响，定义为以滑动区间上的普通导数的积分形式。非定域性（空间）和滞后（时间）行为的同时存在产生了一种新型的热波，这可能具有重要意义。在目前的分析中，Danilovskaya 的问题已经得到解决，其中热冲击作用于无牵引的半空间边界。采用拉普拉斯变换，问题得到了解决，并通过应用黎曼和近似技术实现了时空域的解决方案。根据数值结果对应的图形表示，构建了新理论的结论。显示了几个图形表示来分析不同参数的影响并标记该非局部模型与先前存在的模型的变化。由于存在磁场、记忆相关导数、电位移和时间延迟参数，证明了出色的预测能力，并且还报道了相关长度的影响。