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Volume :31 Issue : 2 2004      Add To Cart                                                                    Download

Fractional extensions of the temperature field

Auther : LYUBOMIR BOYADJIEV’ AND RUDOLF SCHERER2

 1Applied Mathematics and Informatics Department, Technical University of Sofia, P.O.Box 384, 1000 Sofia, Bulgaria,

e-mail: boyadjievl@yahoo.com.

2lnstitule of Practical Mathematics, Universitنt Karisruhe (TH), D-76128 Karisruhe, Germany;
e-mail: scherer@math.uni-karlsruhe. de.

ABSTRACT

The paper is devoted to fractional extensions of the incomplete lumped formulation and the lumped formulation of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the three different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.


Keywords: Caputo’s differintegration operator; fractional heat equation; fractional integrals and derivatives; Laplace transform; Wright function.
MSC 2000: 44A99, 65D99

 

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