Fractional order generalized electro-magneto-thermo-elasticity

• Fractional order generalized electro-magneto-thermoelasticity theories are proposed.
• A unified form of several generalized thermoelasticity theories is introduced.
• The variational theorem and generalized variational principle are established.
• The effect of fractional order on response is evaluated by selected examples.

Built upon the fractional order generalized thermoelasticity (FOGTE), which is based on ETE (extended thermoelasticity), a fractional order generalized electro-magneto-thermo-elasticity (FOGEMTE) theory is developed for anisotropic and linearly electro-magneto-thermo-elastic media by introducing the dynamic electro-magnetic fields, with various generalized thermoelasticity considered, such as ETE, TRDTE (temperature rate dependent thermoelasticity), TEWOED (thermoelasticity without energy dissipation), TEWED (thermoelasticity with energy dissipation), DPLTE (dual-phase-lag thermoelasticity). The two temperature (thermodynamics and conductive temperature) model is also introduced. In addition, to numerically deal with the multi-physics problems expressed by a series of partial differential equations especially a fractional one, the corresponding variational principle based on the variational integral method is proposed, and various degenerated variational theorems are presented. A generalized variational theorem is obtained for the unified theory by using the semi-inverse method. Finally, two examples are numerically validated, and concluding remarks are also given.