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<p>The present study offers a groundbreaking analysis of photo-thermal transport phenomena in semiconductor materials subjected to a mobile heat source. Addressing key limitations of traditional heat transfer theories, this research adopts the Atangana–Baleanu fractional derivative model, which is characterized by a non-singular kernel function. This modern mathematical framework enables a more realistic and accurate depiction of thermal behaviors by capturing the memory-dependent and non-local effects often neglected in classical models.</p><p>Using the Laplace transform technique combined with the eigenvalue approach, the study derives closed-form analytical solutions in the frequency domain. These solutions provide deep insights into the dynamic behavior of several field variables—namely temperature distribution, mechanical displacement, carrier density, and induced thermal stresses. Graphical simulations explore how these quantities evolve under varying parameters such as semiconductor depth, fractional-order values, photo-generated carrier lifetime, and the velocity and intensity of the heat source. One of the most significant outcomes of this investigation is the clear demonstration of the finite speed propagation of thermal waves, a feature that conventional hyperbolic thermoelastic models fail to accurately capture. By incorporating fractional calculus, the study reveals the nuanced and time-dependent nature of thermal interactions in semiconductor media. This distinction underlines the effectiveness of the Atangana–Baleanu model in portraying complex thermophysical phenomena.</p>

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Fractional derivative approach to Opto-thermal energy transmission in semiconductor using spectral analysis method

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Dhyanendra Jain,
  • Uma Tomer,
  • Abdulkafi Mohammed Saeed,
  • Minakshi Tomer,
  • Amita Soni,
  • Anjali Chaudhary

摘要

The present study offers a groundbreaking analysis of photo-thermal transport phenomena in semiconductor materials subjected to a mobile heat source. Addressing key limitations of traditional heat transfer theories, this research adopts the Atangana–Baleanu fractional derivative model, which is characterized by a non-singular kernel function. This modern mathematical framework enables a more realistic and accurate depiction of thermal behaviors by capturing the memory-dependent and non-local effects often neglected in classical models.

Using the Laplace transform technique combined with the eigenvalue approach, the study derives closed-form analytical solutions in the frequency domain. These solutions provide deep insights into the dynamic behavior of several field variables—namely temperature distribution, mechanical displacement, carrier density, and induced thermal stresses. Graphical simulations explore how these quantities evolve under varying parameters such as semiconductor depth, fractional-order values, photo-generated carrier lifetime, and the velocity and intensity of the heat source. One of the most significant outcomes of this investigation is the clear demonstration of the finite speed propagation of thermal waves, a feature that conventional hyperbolic thermoelastic models fail to accurately capture. By incorporating fractional calculus, the study reveals the nuanced and time-dependent nature of thermal interactions in semiconductor media. This distinction underlines the effectiveness of the Atangana–Baleanu model in portraying complex thermophysical phenomena.