Fractional order thermo-viscoelastic theory of biological tissue with dual phase lag heat conduction model

•The fractional linear thermo-viscoelastic theory of biological tissue with dual phase lag model is developed.•The fractional relaxation effects of heat conduction and viscoelastic constitutive relation are considered.•The transient coupling thermal and mechanical behavior of biological tissue is investigated.•The effects of fractional parameters on the responses are discussed. Viscoelasticity is an inherent property of the biological tissue and is often used as a diagnosis parameter in characterizing cancer. Recently, it has been found that fractional calculus agrees well with experimental results when describing the viscoelastic materials. In this study, the fractional linear thermo-viscoelastic theory is developed with considering the fractional relaxation effect of dual phase lag heat conduction model and viscoelastic constitutive relation simultaneously. The transient coupling thermal and mechanical behavior of biological tissue are investigated. The governing equations are solved by Laplace transformation. The effects of fractional parameter on the distributions of temperature, displacement and stress are obtained and illustrated graphically.