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The aim of the contribution is an analysis of time-fractional heat conduction in a sphere with an inner heat source. The object of the consideration is a solid sphere with spherical layer. The heat conduction in the solid sphere and spherical layer is governed by fractional heat conduction equations with Caputo time-derivative. Mathematical (classical) or physical formulations of the Robin boundary condition and the perfect contact of the solid sphere and spherical layer is assumed. The physical boundary condition and the heat flux continuity condition at the interface are expressed by Riemann-Liouville derivative. An analytical solution of the problem under mathematical conditions is determined by using the method of separation of variables and we find the solution in the form of appropriate series. A solution of the problem under physical boundary and continuity conditions is obtained by using the Laplace transform method. The inverse of the Laplace transform by using the Gaver method are numerically determined. Numerical results show the effect of the order of the Caputo derivative occurring in the heat conduction equation and the order of the Riemann-Liouville derivative occurring in the boundary and continuity conditions on the temperature distribution in the sphere.