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Some Fractional Extensions of the Temperature Field Problem in Oil Strata

Boyadjiev, Lyubomir — 2007

Fractional Calculus and Applied Analysis

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...

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

Gogovcheva, ElenaBoyadjiev, Lyubomir — 2005

Fractional Calculus and Applied Analysis

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...

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Nikolova, YankaBoyadjiev, Lyubomir — 2010

Fractional Calculus and Applied Analysis

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.

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

Boyadjiev, LyubomirAl-Saqabi, Bader — 2012

Mathematica Balkanica New Series

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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