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...
2000 Mathematics Subject Classification: 26A33, 33C45
This paper refers to a fractional order generalization of the classical Jacobi
polynomials. Rodrigues’ type representation formula of fractional order
is considered. By means of the Riemann–Liouville operator of fractional
calculus fractional Jacobi functions are defined, some of their properties are
given and compared with the corresponding properties of the classical
Jacobi polynomials. These functions appear as a special case...
Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.
The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is
applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.
MSC 2010: 35R11, 42A38, 26A33, 33E12
The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of...
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