Nonlocal fractional MGT-non-Fourier photothermal model with spatial and temporal nonlocality for controlling the behavior of semiconductor materials with spherical cavities

Mofareh Alhazmi; Ahmed E. Abouelregal; Mofareh Alhazmi; Ahmed E. Abouelregal

doi:10.3934/math.2025348

AIMS Mathematics

2025, Volume 10, Issue 3: 7559-7590. doi: 10.3934/math.2025348

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Nonlocal fractional MGT-non-Fourier photothermal model with spatial and temporal nonlocality for controlling the behavior of semiconductor materials with spherical cavities

Mofareh Alhazmi ,
Ahmed E. Abouelregal ^,

Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
Correction on: AIMS Mathematics 10: 11986–11987.

Received: 27 February 2025 Revised: 22 March 2025 Accepted: 27 March 2025 Published: 31 March 2025
MSC : 74A35, 74D10, 74F05, 93D15

In this work, we present the nonlocal Moore-Gibson-Thompson photothermal (NMGTPT) theory, a novel framework that integrates spatial and temporal nonlocality to address limitations in both traditional and advanced thermoelastic models. Specifically tailored for semiconductor materials with microstructural features, memory effects, and photo-excited phenomena, the NMGTPT theory unifies nonlocal elasticity, MGT thermal relaxation, and photothermal effects to model the complex interplay between heat, deformation, and photo-induced processes. Unlike prior models, the NMGTPT framework incorporates spatial and temporal nonlocalities, enabling the accurate representation of long-range interactions and memory effects. Additionally, the Atangana-Baleanu (AB) fractional operator is integrated into the NMGTPT model to further enhance its ability to describe nonlocal and memory-dependent behavior, making it particularly suitable for advanced material systems. By incorporating a thermal relaxation coefficient, the framework ensures finite-speed thermal wave propagation, effectively addressing the unrealistic prediction of infinite heat speed found in classical models. The theory also integrates photo-excited free carriers, thermal waves, and acoustic waves, proving highly effective in photothermal and photoacoustic studies involving semiconductors. With the inclusion of an internal length scale, the NMGTPT theory successfully captures size-dependent behaviors, which are essential for accurately modeling nanostructured materials, thin films, and composites. This innovation provides a robust platform for investigating the complex dynamics of photothermal and thermoelastic phenomena in advanced material systems.
- photo-excited phenomena,
- nanostructured materials,
- MGT model,
- fractional operator,
- spatial and temporal nonlocality
Citation: Mofareh Alhazmi, Ahmed E. Abouelregal. Nonlocal fractional MGT-non-Fourier photothermal model with spatial and temporal nonlocality for controlling the behavior of semiconductor materials with spherical cavities[J]. AIMS Mathematics, 2025, 10(3): 7559-7590. doi: 10.3934/math.2025348

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Abstract

In this work, we present the nonlocal Moore-Gibson-Thompson photothermal (NMGTPT) theory, a novel framework that integrates spatial and temporal nonlocality to address limitations in both traditional and advanced thermoelastic models. Specifically tailored for semiconductor materials with microstructural features, memory effects, and photo-excited phenomena, the NMGTPT theory unifies nonlocal elasticity, MGT thermal relaxation, and photothermal effects to model the complex interplay between heat, deformation, and photo-induced processes. Unlike prior models, the NMGTPT framework incorporates spatial and temporal nonlocalities, enabling the accurate representation of long-range interactions and memory effects. Additionally, the Atangana-Baleanu (AB) fractional operator is integrated into the NMGTPT model to further enhance its ability to describe nonlocal and memory-dependent behavior, making it particularly suitable for advanced material systems. By incorporating a thermal relaxation coefficient, the framework ensures finite-speed thermal wave propagation, effectively addressing the unrealistic prediction of infinite heat speed found in classical models. The theory also integrates photo-excited free carriers, thermal waves, and acoustic waves, proving highly effective in photothermal and photoacoustic studies involving semiconductors. With the inclusion of an internal length scale, the NMGTPT theory successfully captures size-dependent behaviors, which are essential for accurately modeling nanostructured materials, thin films, and composites. This innovation provides a robust platform for investigating the complex dynamics of photothermal and thermoelastic phenomena in advanced material systems.

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