arXiv subjects

Doniyor Usmonov

Publications and source records attributed to Doniyor Usmonov.

3 recordsLinked to original sources

arXiv2026

Nonlocal problem for multi-parametric integral-differential equation

This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial integral expressions of the unknown function with continuous kernels. Using a known representation of the solution to the corresponding Goursat problem in terms of bivariate and trivariate Mittag-Leffler-type functions, the problem is reduced to a system of Volterra integral equations of the second kind for boundary traces. Based on this reduction, sufficient conditions ensuring existence and uniqueness of the solution are established. An explicit representation of the solution is also obtained via the solution of the derived integral system.

math.AP↗

arXiv2026

Green's Function Framework for Boundary Value Problems with the Regularized Prabhakar Fractional Derivative

In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the superposition method. An explicit representation of the solution and the corresponding Green's function is obtained. The explicit form of the Green's function is expressed in terms of a bivariate Mittag-Leffler type function. Then, it is proved that the obtained solution indeed constitutes the solution of the considered problem.

math.AP↗

arXiv2026

Green's Function and Solution Representation for a Boundary Value Problem Involving the Prabhakar Fractional Derivative

We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler functions, we reduce the problem to a Volterra-type integral equation. This reduction enables the explicit construction of the corresponding Green's function. Based on the obtained Green's function, we derive a closed-form integral representation of the solution and prove its existence and uniqueness. The results extend classical Green-function techniques to a wider class of fractional operators and provide analytical tools for further study of boundary and inverse problems associated with Prabhakar-type fractional differential equations.

math.AP↗