In this paper, the inverse problem of determining convolution kernel in the time-fractional wave equation with the Caputo derivative is studied. To express the solution of the Cauchy problem, the fundamental solution of the corresponding equation is systematically formulated, with a detailed investigation into the properties of this solution. The fundamental solution contains a Fox's function, which is widely used in the theory of diffusion-wave equation. Using the formulas of asymptotic expansionsfor the fundamental solution and its derivatives, an estimate for the solution of the direct problem isobtained. A priori estimate contains the norm of the unknown kernel function and it was used for studying the inverseproblem. The inverse problem is reduced to the equivalent integral equation, By the fixed point argument in suitable functional classes the local solvability is proven. The global uniqueness results and also the stability estimate for solution to the inverse problem are established.
| Mualliflar | Durdiev Durdimurod, Subhonova Ziyoda |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 50-63 |
| DOI | 10.29229/uzmj.2025-3-5 |
DOI: 10.29229/uzmj.2025-3-5 · Maqolaning asl sahifasi
Gerasimov-Caputo fractional derivative, Fox’s H-function, Mittag-Leffler function, integral equation.
This article studies the inverse problem of finding a multiplier on the right-hand side, depending on the spatial variable $x$. In the direct problem, an initial-boundary value problem for a fourth-order differential…
The mathematical model of the control system considered in this paper is presented in the form of a linear nonstationary differential inclusion. For this model of the control system, the problem of locally relative…
In this paper, hypergeometric function of Lauricella $F_{A}^{(n)}$ has been investigated. The new properties of which are established and applied to the solution of the Dirichlet problem for the three-dimensional…
Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these…
We study a differential game of two pursuers and one evader, whose dynamics are described by linear differential equations, in $\mathbb{R}^n$. The control functions of pursuers and evader are subjected to the Grönwall…
In this paper we study a global stability problem for polynomial stochastic operators associated with higher-order diagonally primitive doubly stochastic hyper-matrices.
In approximate integration, an interesting and relevant problem is the construction of formulas with a minimum number of nodes for a given algebraic degree of accuracy.
This paper constructs a discrete analogue of the second-order differential operator with variable coefficient. The construction is based on harrow-shaped functions and the application of direct and inverse Fourier…
Let $G~$be finite Jordan domain bounded a Dinismooth curve $\Gamma ~$in the complex plane. Marcinkiewiczmultiplierand Littlewood-Paley type theorems in Smirnov-Orliczclasses, defined in domain $G$, are proved.
The well-known classical Dirichlet problem states that if $D\subset {\mathbb R}^{n}$ is a regular domain, then for any continuous function $\varphi (\xi )\in C(\partial D)$, there exists a unique harmonic function…