TY  - JOUR
A1  - Petreska, Irina
A1  - de Castro, Antonio S. M.
A1  - Sandev, Trifce
A1  - Lenzi, Ervin K.
T1  - The time-dependent Schrödinger equation in non-integer dimensions for constrained quantum motion
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - We propose a theoretical model, based on a generalized Schroedinger equation, to study the behavior of a constrained quantum system in non-integer, lower than two-dimensional space. The non-integer dimensional space is formed as a product space X x Y, comprising x-coordinate with a Hausdorff measure of dimension alpha(1) = D -1 (1 < D < 2) and y-coordinate with the Lebesgue measure of dimension of length (alpha(2) = 1). Geometric constraints are set at y = 0. Two different approaches to find the Green's function are employed, both giving the same form in terms of the Fox H-function. For D = 2, the solution for two-dimensional quantum motion on a comb is recovered. (C) 2020 Elsevier B.V. All rights reserved.
KW  - Schrödinger equation
KW  - non-integer dimension
KW  - Green's function
KW  - Bessel functions
KW  - Fox H-function
Y1  - 2020
U6  - https://doi.org/10.1016/j.physleta.2020.126866
SN  - 0375-9601
SN  - 1873-2429
VL  - 384
IS  - 34
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Tomovski, Zivorad
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Dubbeldam, Johan
T1  - Generalized space-time fractional diffusion equation with composite fractional time derivative
JF  - Physica : europhysics journal ; A, Statistical mechanics and its applications
N2  - We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
KW  - Fractional diffusion equation
KW  - Composite fractional derivative
KW  - Riesz-Feller fractional derivative
KW  - Mittag-Leffler functions
KW  - Fox H-function
KW  - Fractional moments
KW  - Asymptotic expansions
KW  - Grunwald-Letnikov approximation
Y1  - 2012
U6  - https://doi.org/10.1016/j.physa.2011.12.035
SN  - 0378-4371
SN  - 1873-2119
VL  - 391
IS  - 8
SP  - 2527
EP  - 2542
PB  - Elsevier
CY  - Amsterdam
ER  -