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<p>In this work, we investigate a two-dimensional modified fractional-order dual-phase-lag (DPL) thermoelastic problem in a half-space medium subjected to both stationary and moving heat sources. The model incorporates three distinct thermal relaxation times and employs Caputo-type fractional derivatives to capture memory effects in the time domain. The governing partial differential equations are reduced to a system of ordinary differential equations using harmonic wave-type transformations. These equations are formulated in vector–matrix form and solved analytically via the eigenvalue approach. Closed-form expressions for displacement, stress, and temperature fields are obtained under various generalized thermoelasticity frameworks, including Green–Lindsay (GL) and dual-phase-lag (DPL) theories. Numerical simulations are carried out using MATLAB to illustrate the influence of fractional-order parameters, relaxation times, and the nature of the heat source on the resulting thermoelastic responses. The results provide insights into the behavior of fractional dual-phase-lag models and their applicability in describing complex thermal–mechanical interactions in elastic continua.</p>

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Analysis of fractional-order thermoelasticity with a heat source and three relaxation times

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Sourov Roy,
  • Abhijit Lahiri

摘要

In this work, we investigate a two-dimensional modified fractional-order dual-phase-lag (DPL) thermoelastic problem in a half-space medium subjected to both stationary and moving heat sources. The model incorporates three distinct thermal relaxation times and employs Caputo-type fractional derivatives to capture memory effects in the time domain. The governing partial differential equations are reduced to a system of ordinary differential equations using harmonic wave-type transformations. These equations are formulated in vector–matrix form and solved analytically via the eigenvalue approach. Closed-form expressions for displacement, stress, and temperature fields are obtained under various generalized thermoelasticity frameworks, including Green–Lindsay (GL) and dual-phase-lag (DPL) theories. Numerical simulations are carried out using MATLAB to illustrate the influence of fractional-order parameters, relaxation times, and the nature of the heat source on the resulting thermoelastic responses. The results provide insights into the behavior of fractional dual-phase-lag models and their applicability in describing complex thermal–mechanical interactions in elastic continua.