Geodesic
Some Fractional Extensions of the Temperature Field Problem in Oil Strata
Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 75-98.

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This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier 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 different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.
Keywords: Caputo Differintegration Operator, Fractional Heat Equation, Fractional Integrals and Derivatives, Laplace Transforms, Wright’s Function, 44A99, 65D99 
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Boyadjiev, Lyubomir. Some Fractional Extensions of the Temperature Field Problem in Oil Strata. Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 75-98. http://geodesic.mathdoc.fr/item/FCAA_2007_10_1_a4/