Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function

2000 Mathematics Subject Classification: 26A33, 33C45

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Operational Calculi for the Euler Operator

2000 Mathematics Subject Classification: 44A40, 44A35

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63

q-Heat Operator and q-Poisson’s Operator

2000 Mathematics Subject Classification: 33D15, 33D90, 39A13

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

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.

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55