Applying Caputo and Caputo–Fabrizio fractional derivatives on a viscothermoelastic circular microplate under Lord–Shulman theorem

This study introduces a novel mathematical model to investigate heat conduction through a circular micro-plate that is isotropic, homogeneous, and viscothermoelastic. Based on the Kirchhoff–Love plate hypothesis, the governing differential equations have been formulated in the context of the Lord–Shulman theory of generalized thermoelasticity. This model aims to integrate Young’s modulus with fractional operators of the derivative, namely, the Caputo and Caputo–Fabrizio operators, with the conventional derivative. The research illustrates the implementation of scaled viscothermoelasticity on a circular microplate that is simply supported at both extremities. The microplate’s boundary has undergone thermal loading using ramp-type heating. Numerical computations have been conducted to ascertain the inverse of the Laplace transform. The research included graphical comparisons of the definitions of fractional and ordinary derivatives. The effects of the fractional-order and thickness parameters on the thermal wave distribution are deemed minimal; however, the impact of the ramp-time heat parameter is significant. The fractional-order parameter substantially influences the mechanical waves. The ramp heat parameter effectively regulates energy dissipation in ceramic resonators.