Fractional Order Thermoelastic Wave Assessment in a Nanoscale Beam Using the Eigenvalue Technique

  • I. Abbas
  • F. Alzahrani
  • A. N. Abdalla
  • F. BertoEmail author

This paper presents an analytical approach associated with Laplace transforms and a sequential concept over time to obtain the increment of temperature in nanoscale beam with fractional order heat conduction clamped from both ends. The governing equations are written in the forms of differential equations of matrix-vector in the domain of the Laplace transforms and are then solved by the eigenvalue technique. The analytical solutions are obtained for the increment of temperature, displacement, lateral deflection, and stresses in the Laplace domain. Numerical simulations are provided for silicon-like nanoscale beam material, with graphical display of calculated results. The physical implications of distributions of physical variables considered in this article are discussed.


Laplace transforms nanoscale beam fractional order eigenvalues approach 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • I. Abbas
    • 1
    • 2
  • F. Alzahrani
    • 2
  • A. N. Abdalla
    • 1
  • F. Berto
    • 3
    Email author
  1. 1.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt
  2. 2.Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of Engineering Design and MaterialsNorwegian University of Science and Technology (NTNU)TrondheimNorway

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