Fractional order theory of thermo-viscoelasticity and application

In this work, we derive a new fractional order theory for thermo-viscoelasticity. A uniqueness theorem for these equations is proved. A reciprocity theorem is also proved. A 1D problem for a viscoelastic half space is solved by using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained by using a numerical method. The temperature, displacement and stress distributions are computed and represented graphically.