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Fractional extensions of the temperature field problems in oil strata. (English) Zbl 1110.76050
Summary: We consider fractional extensions of the incomplete lumped formulation and the lumped formulation of temperature field problems in oil strata. Laplace transform is used to solve the corresponding heat equations with an additional term representing the internal heat sources. Efros theorem, a generalized form of Laplace convolution, is used to obtain an analytic solutions. Special cases are mentioned.

MSC:
76S05 Flows in porous media; filtration; seepage
26A33 Fractional derivatives and integrals
80A20 Heat and mass transfer, heat flow (MSC2010)
86A05 Hydrology, hydrography, oceanography
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