Thermoelasticity based on time-fractional heat conduction equation in spherical coordinates

The fundamental solutions to the first and second Cauchy problems and to the source problem are obtained for central symmetric time-fractional heat conduction equation in an infinite medium in spherical coordinates. Radial heat conduction in a sphere and in an infinite solid with a spherical cavity is investigated. TheDirichlet boundary problem with the prescribed boundary value of temperature and the physical Neumann boundary problem with the prescribed boundary value of the heat flux are solved using the integral transform technique. The associated thermal stresses are studied. The numerical results are illustrated graphically for the whole spectrum of order of fractional derivative. © Springer International Publishing Switzerland 2015.