Caputo Differintegration Operator Fractional Heat Equation Fractional Integrals and Derivatives Laplace Transforms Wright’s Function 44A99 65D99
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 10, No 1, (2007), 75p-98p
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.