Abstract
This work proposed a modified heat conduction model with fractional order, including the Caputo-Fabrizio fractional derivative without a singular kernel. Based on the generalized thermoelasticity with two-phase delays, Maxwell equations, and Kelvin-Voigt type, along with the Euler-Bernoulli beam theories, the governing equations have been constructed. The aim of this article is to present a novel model to explain the thermoelastic behavior of viscoelastic beams, considering the effects of temperature increment and the magnetic field, and to address the deficiencies that appeared in some other theories of fractional order. The newly constructed model has been applied to address the problem of perfectly conducting microbeam exposed to laser heat treatment. For the final solution, an integral transformation methodology has been employed. The final solution of the problem is achieved by employing a numerical approach and computer programming. The influence of various factors, such as fractional order parameter, and viscoelastic properties, has been examined graphically and studied in detail.