Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Spherical Coordinates

The fundamental solutions to the firstFirst Cauchy problem and second Cauchy problemsSecond Cauchy problem and to the source problemSource problem are obtained for the central symmetric time-fractional heat conduction equationFractional heat conduction equation in an infinite medium in spherical coordinatesSpherical coordinates. Radial heat conduction in a sphereSphere and in an infinite solid with a spherical cavity is investigated. The Dirichlet boundary conditionsDirichlet boundary condition with the prescribed boundary value of temperature and the physical Neumann boundary conditionPhysical Neumann boundary condition with the prescribed boundary value of the heat flux are solved using the integral transform technique. The time-harmonic source term and the time-harmonic boundary conditionsBoundary condition are considered. The associated thermal stresses are studied. The numerical results are illustrated graphically for the whole spectrum of order of fractional derivative.