On a fractional order generalized thermo-elastic diffusion theorem. (English) Zbl 1469.35230

Summary: In this work, a new theory of thermo-diffusion in elastic solids is derived using the methodology of fractional calculus. The theories of coupled thermo-elastic diffusion and of generalized thermo-elastic diffusion problem with one relaxation time and also of generalized thermo-elastic diffusion in GN models follow as limit cases. A uniqueness and reciprocity theorem for these equations are derived using Laplace transform technique on the assumption of symmetry of stress tensor and positivity of associated parameters. Finally, a variational theorem is obtained for the governing equations.


35R11 Fractional partial differential equations
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
74A15 Thermodynamics in solid mechanics
74F05 Thermal effects in solid mechanics
80A19 Diffusive and convective heat and mass transfer, heat flow
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