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Bakhodirjon Toshtemirov

Publications and source records attributed to Bakhodirjon Toshtemirov.

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↗
arXiv2021

Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators

In this paper, we consider a nonlocal boundary-value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional derivative in a rectangular domain. The main target of this work is to analyze the uniqueness and the existence of the solution of the considered problem by means of eigenfunctions. Moreover, we construct the solution of the ordinary fractional differential equation with the right-sided bi-ordinal Hilfer derivative by the method of reduction to the Volterra integral equation. Then, we present sufficient conditions for given data in order to show the existence of the solution.

math.AP↗