Fractional-order generalized thermoelastic diffusion theory

• DOI: 10.1007/s10483-017-2230-9
• Publication Date: 2017-06-06T05:37:24Z
• Authors: Chunbao Xiong; Yanbo Niu
• Keywords: 0101 mathematics; 01 natural sciences

The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by a sequence of incomplete differential equations, particularly by a fractional equation, a generalized variational principle is obtained for the unified theory using a semi-inverse method. In numerical implementation, the dynamic response of a semi-infinite medium with one end subjected to a thermal shock and a chemical potential shock is investigated using the Laplace transform. Numerical results, i.e., non-dimensional temperature, chemical potential, and displacement, are presented graphically. The influence of the fractional order parameter on them is evaluated and discussed.