Abstract
In this work, a new theory of thermoelasticity has been derived based on fractional order of strain (fraction order Duhamel-Neumann stress-strain relation). A new unified system of differential equations that govern seven different models of thermoelasticity in the context of one temperature type and two-temperature types (14 different models of thermoelasticity) has been constructed. The second part of this work, applications of thermoelasticity with fractional order strain for an isotropic and homogenous one-dimensional elastic half-space based on one-temperature thermoelasticity of Biot, Lord-Shulman, Green-Lindsay and Green-Naghdi type II models have been solved.