Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

In this work, we study a problem in a fractional order theory of thermoelastic diffusion in an infinite medium with a spherical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity. The chemical potential is assumed a known function of time on the bounding cavity. The form of vector–matrix differential equation in the Laplace transform domain, the basic equations have been written, which is then solved by an eigenvalue technique. The analytical solution in the Laplace domain is obtained for the displacement, the temperature, the concentration, the stress components and chemical potential. Numerical results represented graphically.