Abstract
A new fractional relaxation operator is derived using the methodology of fractional calculus. The governing coupled fractional differential equations in the frame of the thermo-viscoelasticity with fractional order heat transfer are applied to the one-dimensional problem with heat sources. Laplace transform and state space techniques are used to get the solution. According to the numerical results and its graphs, conclusion about the new theory of thermo-viscoelasticity has been constructed. The theories of coupled thermo-viscoelasticity and of generalized thermo-viscoelasticity with one relaxation time follow as limit cases.