arXiv subjects

Shavkat Alimov

Publications and source records attributed to Shavkat Alimov.

3 recordsLinked to original sources

arXiv2024

On determining the fractional exponent of the subdiffusion equation

Determining the unknown order of the fractional derivative in differential equations simulating various processes is an important task of modern applied mathematics. In the last decade, this problem has been actively studied by specialists. A number of interesting results with a certain applied significance were obtained. This paper provides a short overview of the most interesting works in this direction. Next, we consider the problem of determining the order of the fractional derivative in the subdiffusion equation, provided that the elliptic operator included in this equation has at least one negative eigenvalue. An asymptotic formula is obtained according to which, knowing the solution at least at one point of the domain under consideration, the required order can be calculated.

math.AP↗

arXiv2021

Inverse problem of determining an order of the Riemann-Liuville time-fractional derivative

The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using the classical Fourier method it is proved, that the value of the norm jju(t)jj of the solution at a_xed time instance recovers uniquely the order of derivative. A list of examples is discussed, including a linear system of fractional di_erential equations, di_erential models with involution, fractional Sturm-Liouville operators, and many others.

math.GM↗

arXiv2019

An Application of Abel's Method to the Inverse Radon Transform

A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out. Geometric properties of the kernel and their implications for computer implementation are discussed. Suggestions are made for applications and an example is presented.

math.NA↗