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**A study on fractional order magneto-thermoelasticity with three-phase-lag.**
*(English)*
Zbl 1367.74005

Summary: In this work, we consider a two-dimensional fractional order generalized thermoelastic problem in a homogeneous, isotropic and perfectly conducting thermoelastic half-space subjected to a moving load. The surface of half-space is initially placed in an external magnetic field with constant intensity and therefore, Maxwell’s theory of electrodynamics has been effectively introduced. The basic governing equations of the problem are derived in the context of fractional order three phase lag model of generalized thermoelasticity [M. A. Ezzat et al., Arch. Appl. Mech. 82, No. 4, 557–572 (2012; Zbl 1293.74073)]. The formulation is solved by using Laplace-Fourier transform technique and inversion is carried out numerically. Numerical results are computed and represented graphically for the displacement, temperature and stress distributions. Effects of fractional order parameter and magnetic field on the different thermoelastic fields are analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present
investigation.

### MSC:

74A15 | Thermodynamics in solid mechanics |

74F15 | Electromagnetic effects in solid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |