  In the present paper, we solve three boundary value problems related to the
temperature field in oil strata -- the fractional extensions of the incomplete
lumped formulation and lumped formulation in the linear case and the fractional
generalization of the incomplete lumped formulation in the radial case. By
using the Caputo differintegral operator and the Laplace transform, the
solutions are obtained in integral forms where the integrand is expressed in
terms of the convolution of some auxiliary functions of Wright function type. A
generalization of the Laplace transform convolution theorem, known as Efros'
theorem is widely used.
