For the first time, numerical solutions were computed using fractional-order strain considerations in the current study. For an isotropic and homogeneous nanobeam, the thermoelasticity with one relaxation time and fractional-order strain theory based on Caputo–Fabrizio’s definition of fractional derivative was examined. With thermal loading and in simply supported boundary conditions, the Laplace transformations have been used upon the governing equations and its inversion was computed using the Tzou technique approximation. The numerical calculations for a thermoelastic rectangular gold (Au) nanobeam have been validated as a model where ramp-type heat is considered. The computational solutions have been depicted in two-dimensions graphs for several situations to investigate the impact of the fractional-order and ramping heat parameters on all of the functions studied. The temperature increment distribution, lateral vibration, deformation, tension, and energy density are all influenced by fractional-order and ramp-time heat parameters. The ramp-time heat parameter might be utilized to regulate nanobeam vibration and energy damping in thermoelastic nanobeams.
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