Approximate Analytical Solutions of Creeper-Type Fractional Maxwell–Faraday Systems with Piezoelectric Effects

We present newly derived approximate analytical solutions (AAS) of the motion, free and forced modes of dynamics of two viscoelastic rheological Maxwell–Faraday discrete dynamic systems (RMFDDSFTPEP), creeper type, and fractional type, with piezoelectric polarization property of the Faraday piezoelectric element. They always occur in paired rheological discrete dynamic systems depending on the order of sparse coupling of rheological basic light elements in standard light-binding structures and their connections with the rigid body and the fixed point. The research results presented in the paper AAS for the creep-flow EFM of creep-flow dynamics of a RMFDDSFTPEP, which characterizes the SLFTMF coupling set of models, which includes piezoelectric effects. To avoid the inversion of complex, fractional-order expressions of the Laplace transforms (LT), the terms of the complex expressions are expanded into power orders, based on the assumption that certain ratios are small relative to unity. The inverse LT is performed term by term to obtain AAS in the time domain.