International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 10, Pages 1577-1588
doi:10.1155/IJMMS.2005.1577

On the Lauwerier formulation of the temperature field problem in oil strata

Lyubomir Boyadjiev,1 Ognian Kamenov,2 and Shyam Kalla3

1Institut für Praktische Mathematik, Universität Karlsruhe (TH), Karlsruhe 76128, Germany
2Department of Applied Mathematics and Informatics, Technical University of Sofia, P.O. Box 384, Sofia 1000, Bulgaria
3Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 13 January 2005

Copyright © 2005 Lyubomir Boyadjiev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). The boundary value problem for the fractional heat equation is solved by means of the Caputo differintegration operator D∗(α) of order 0<α≤1 and the Laplace transform. The solution is obtained in an integral form, where the integrand is expressed in terms of a convolution of two special functions of Wright type.