With the rapid development and application of ultra-short pulses in the micro-machining of viscoelastic structures, the transient thermodynamic response at the micro/nano scale have become of great importance. Increasingly crucial at the microscale are the scale and memory effects in elastic deformation and heat transfer. A multitude of experimental and theoretical studies indicate that, for practical analyses, the thermal conductivity of materials ought not to be treated as a fixed value. This work aims to formulate a thermoviscoelastic model by incorporating a fractional-order three-phase-lag heat conduction model. The proposed framework utilizes the Atangana-Baleanu definition of fractional derivative, which features a non-singular kernel, along with an extended Caputo definition to describe the time-dependent characteristics of heat conduction. Additionally, the nonlocal elasticity model is taken into account in the stress-strain relationships. Then, the modified model is applied to investigate the nonlinear electro-magneto-thermo-viscoelastic response of a polymer spherical nanoshell with variable thermal conductivity subjected to ramp-type heating load under the effect of a magnetic field. Taking into account the variable thermal conductivity, the nonlinear governing equations are derived. Employed to derive and solve the governing equations are the Laplace and Kirchhoff transformations. In-depth discussions are carried out regarding the influences of diverse factors such as the fractional-order parameter, the nonlocal parameter and the variable thermal conductivity on physical quantities.
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