Acta Mechanica

, Volume 230, Issue 1, pp 179–199 | Cite as

Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative

  • S. Mondal
  • P. Pal
  • M. KanoriaEmail author
Original Paper


Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of a non-Gaussian pulsed laser type heat source in a stress free isothermal half-space in the context of Lord–Shulman (LS), dual-phase lag (DPL), and three-phase lag (TPL) theories of thermoelasticity simultaneously. The memory-dependent derivative is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace transform as a tool, the problem has been transformed to the space-domain, and it is then solved analytically. To get back all the thermophysical quantities as a function of real time, we use two Laplace inversion formulas, viz. Fourier series expansion technique (Honig in J Comput Appl Math10(1):113–132, 1984) and Zakian method (Electron Lett 6(21):677–679, 1970). According to the graphical representations corresponding to the numerical results, a comparison among LS, DPL, and TPL model has been studied in the presence and absence of a memory effect simultaneously. Moreover, the effects of a laser pulse have been studied in all the thermophysical quantities for different kernels (randomly chosen) and different delay times. Then, the results are depicted graphically. Finally, a comparison of results, deriving from the two numerical inversion formulas, has been made.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBasirhat CollegeBasirhatIndia
  2. 2.Department of Applied MathematicsUniversity of CalcuttaKolkataIndia

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