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Fractional Order GN Model on Photo-Thermal Interaction in a Semiconductor Plane

  • Aatef HobinyEmail author
  • Ibrahim Abbas
Original Paper


A mathematical model of Green–Naghdi photothermal theory based on fractional-order of heat transfer is given to study the wave propagation in a two-dimensional semiconductor material. Closed-form analytical solutions to obtain the physical quantities subjected to a heat flux with a pulse that decays exponentially in the surface of semiconductor half-space are presented. Through the use of Laplace and Fourier transforms with the methodology of eigenvalues techniques, the analytical solutions of all physical quantities are obtained. A semiconductor medium such as silicon is studied. The derived method is evaluated with numerical results which are applied to the semiconductor medium in simplified geometry. The significant influence of time-fractional derivative parameters are discussed for all physical quantities. Suitable discussions and conclusions are presented.


Laplace-Fourier transforms Fractional GN model Photo-thermal waves Eigenvalues approach 


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This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (KEP-24-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of mathematics, Faculty of ScienceSohag UniversitySohagEgypt

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