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.