Sabir Umarov - Academia.edu (original) (raw)

Papers by Sabir Umarov

Physics Letters, Jul 1, 2008

Nucleation and Atmospheric Aerosols, 2007

arXiv (Cornell University), Nov 10, 2010

arXiv (Cornell University), Oct 15, 2015

$Research paper thumbnail of Random walk models associated with distributed fractional order differential equations$

Institute of Mathematical Statistics eBooks, 2006

Milan Journal of Mathematics, Mar 14, 2008

$Research paper thumbnail of Generalization of symmetric <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>α-stable Lévy distributions for <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mo>></mo><mn>1</mn></mrow><annotation encoding="application/x-tex">q>1</annotation></semantics></math>q>1$

arXiv (Cornell University), Nov 12, 2009

$Research paper thumbnail of Symmetric <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>q</mi><mo separator="true">,</mo><mi>α</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(q,\alpha)</annotation></semantics></math>(q,α)-Stable Distributions. Part I: First Representation$

arXiv (Cornell University), Jun 1, 2006

Physica D: Nonlinear Phenomena, Feb 1, 2019

Journal of Mathematical Physics, 2010

$Research paper thumbnail of Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion$

Proceedings of the American Mathematical Society, Feb 1, 2011

Fractal and Fractional

A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, wel... more A nonlocal boundary value problem for the fractional version of the Rayleigh–Stokes equation, well-known in fluid dynamics, is studied. Namely, the condition u(x,T)=βu(x,0)+φ(x), where β is an arbitrary real number, is proposed instead of the initial condition. If β=0, then we have the inverse problem in time, called the backward problem. It is well-known that the backward problem is ill-posed in the sense of Hadamard. If β=1, then the corresponding non-local problem becomes well-posed in the sense of Hadamard, and moreover, in this case a coercive estimate for the solution can be established. The aim of this work is to find values of the parameter β, which separates two types of behavior of the semi-backward problem under consideration. We prove the following statements: if β≥1, or β<0, then the problem is well-posed; if β∈(0,1), then depending on the eigenvalues of the elliptic part of the equation, for the existence of a solution an additional condition on orthogonality of the...

$Research paper thumbnail of On fractional Duhamel's principle and its applications$

arXiv: Classical Analysis and ODEs, Apr 13, 2010

Developments in Mathematics, 2015

In Section 5.6 we studied the existence of a solution to the multi-point value problem for a frac... more In Section 5.6 we studied the existence of a solution to the multi-point value problem for a fractional order pseudo-differential equation with m fractional derivatives of the unknown function. This is an example of fractional distributed order differential equations. Our main purpose in this chapter is the mathematical treatment of boundary value problems for general distributed and variable order fractional differential-operator equations. We will study the existence and uniqueness of a solution to initial and multi-point value problems in different function spaces.

In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with so... more In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor? - is studied for the whole range of q∈ (-∞, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q > 1, excluding two particular cases of q<1, namely, q = 1/2 and q = 2/3, which are also out of the theory valid for q > 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.