arXiv subjects

Azizbek Mamanazarov

Publications and source records attributed to Azizbek Mamanazarov.

3 recordsLinked to original sources

arXiv2026

Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients

In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation of variables, we establish the existence of eigenvalues and eigenfunctions for the associated spectral problem and prove that the operator possesses a discrete spectrum. Additionally, we establish the relationship between the given data and the unique solvability of the problem, offering new insights into how degeneracy influences fractional diffusion processes.

math.AP↗

arXiv2024

Inverse coefficient problems for the heat equation with fractional Laplacian

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data and recovering the space-dependent source function of the fractional heat equation.

math.AP↗

arXiv2022

The Prabhakar fractional $q$-integral and $q$-differential operators, and their properties

In this paper, we have introduced the Prabhakar fractional $q$-integral and $q$-differential operators. We first study the semi-group property of the Prabhakar fractional $q$-integral operator, which allowed us to introduce the corresponding $q$-differential operator. Formulas for compositions of $q$-integral and $q$-differential operators are also presented. We show the boundedness of the Prabhakar fractional $q$-integral operator in the class of $q$-integrable functions.

math.AP↗