In this paper, we investigate a time-fractional diffusion-wave equation, where the classical second-order time derivative is replaced by a fractional derivative of order $\rho \in (1,2)$. We consider a class of non-local boundary value problems involving four real parameters $\alpha_1$, $\alpha_2$, $\beta_1$, and $\beta_2$ under general conditions. Using the Fourier method in an abstract Hilbert space setting, we derive necessary and sufficient conditions for the well-posedness of the problem. We prove that the solution exists and is unique if certain algebraic conditions on the parameters are satisfied. In cases where these conditions fail, we describe the structure of the solution and show that uniqueness may be lost. For such cases, we also formulate orthogonality conditions that guarantee existence.
| Mualliflar | Ashurov R., Nuraliyeva N.Sh. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-05 |
| Jild | 69 |
| Son | 3 |
| Betlar | 25-38 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-3 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-3 · Maqolaning asl sahifasi
Fourier method, abstract operator, complete system, non-local problems, Caputo derivatives.
| APA | Ashurov R., & Nuraliyeva N.Sh. (2025). A Four-Parameter non-local Problem for a Fractional Wave Equation. O‘zbekiston matematika jurnali, 69(3), 25-38. https://doi.org/10.29229/uzmj.2025-3-3 |
|---|---|
| GOST (OAK) | Ashurov R., Nuraliyeva N.Sh. A Four-Parameter non-local Problem for a Fractional Wave Equation // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 25-38. – DOI: 10.29229/uzmj.2025-3-3. |
| MLA | Ashurov R., and Nuraliyeva N.Sh. “A Four-Parameter non-local Problem for a Fractional Wave Equation.” O‘zbekiston matematika jurnali, 69(3), 25-38, 2025. https://doi.org/10.29229/uzmj.2025-3-3 |
| Chicago | Ashurov R., and Nuraliyeva N.Sh. “A Four-Parameter non-local Problem for a Fractional Wave Equation.” O‘zbekiston matematika jurnali, 69(3), 25-38 (2025). https://doi.org/10.29229/uzmj.2025-3-3 |
| Harvard | Ashurov R., and Nuraliyeva N.Sh (2025) ‘A Four-Parameter non-local Problem for a Fractional Wave Equation’, O‘zbekiston matematika jurnali, 69(3), 25-38. https://doi.org/10.29229/uzmj.2025-3-3 |
| BibTeX | @article{ashurovr2025,
title = {A Four-Parameter non-local Problem for a Fractional Wave Equation},
author = {Ashurov R. and Nuraliyeva N.Sh.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {25-38},
doi = {10.29229/uzmj.2025-3-3},
url = {https://doi.org/10.29229/uzmj.2025-3-3}
} |
Boshqa maqola uchun iqtibos tayyorlash
In this paper, we study $p$-adic quasi-Gibbs measures forthe three-state SOS model on a Cayley tree of order two. The existence ofnew translation-invariant $p$-adic quasi-Gibbs measures have been found.Moreover, the…
In the present paper in $L_2^{(m)}(-1,1)$ space an optimal quadrature formula is constructed for approximate calculation of the Cauchy type singular integral. Explicit formulas for the optimal coefficients are obtained.
In this work, the complex Lie affgebra structures on three-dimensional solvable Lie algebras are completely determined
In this paper we obtain the criterion of weak convergence of the sequence of the sum of the first $n$ terms of the linear process $\left\{X_{kn} ,\; k=1,2,...,n;\; n=1,2,...\right\}$ with random coefficients…
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…
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…
In this paper we study a global stability problem for polynomial stochastic operators associated with higher-order diagonally primitive doubly stochastic hyper-matrices.
O‘zbekiston matematika jurnali — barcha maqolalar · 2025-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.