Nonlocal problems for sub-diffusion equation in a rectangular domain

Toshbuvayeva, Odinaxon

FarDU ilmiy xabarlari · 2026-yil

Annotatsiya

In this paper, we investigate nonlocal boundary value problems for a time-fractional sub-diffusion equation in a rectangular domain. Two classes of nonlocal conditions are considered: a pointwise nonlocal boundary condition and an integral nonlocal boundary condition. By employing the Green function method, the considered problems are reduced to Volterra integral equations of the second kind with weakly singular kernels. The properties of the corresponding kernels are studied in detail, and their continuity and boundedness are established. Using the theory of Volterra integral equations, we prove the existence and uniqueness of continuous solutions to both nonlocal problems. The obtained results extend the classical boundary value problems for fractional diffusion equations and provide a theoretical basis for the analysis of nonlocal processes with memory effects.

Maqola ma’lumotlari
MualliflarToshbuvayeva, Odinaxon
JurnalFarDU ilmiy xabarlari
NashriyotFarg‘ona davlat universiteti
ISSN2010-8419, 2181-1571
Nashr sanasi2026-10-10
Jild7
Son5
TilIngliz
Indeksga qo‘shilgan2026-10-11

Maqolaning asl sahifasi

Kalit so‘zlar

time-fractional diffusion equation; sub-diffusion process; nonlocal boundary condition; Green function; Volterra integral equation; existence and uniqueness., time-fractional diffusion equation; sub-diffusion process; nonlocal boundary condition; Green function; Volterra integral equation; existence and uniqueness.

Iqtibos keltirish

APAToshbuvayeva, Odinaxon (2026). NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN. FarDU ilmiy xabarlari, 7(5). https://journal.fdu.uz/main/article/7762
GOST (OAK)Toshbuvayeva, Odinaxon NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN // FarDU ilmiy xabarlari. – 2026. – T. 7, № 5.
MLAToshbuvayeva, Odinaxon. “NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN.” FarDU ilmiy xabarlari, 7(5), 2026. https://journal.fdu.uz/main/article/7762
ChicagoToshbuvayeva, Odinaxon. “NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN.” FarDU ilmiy xabarlari, 7(5) (2026). https://journal.fdu.uz/main/article/7762
HarvardToshbuvayeva, Odinaxon (2026) ‘NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN’, FarDU ilmiy xabarlari, 7(5). https://journal.fdu.uz/main/article/7762
BibTeX
@article{toshbuvayevaodinaxon2026,
  title = {NONLOCAL PROBLEMS FOR SUB-DIFFUSION EQUATION IN A RECTANGULAR DOMAIN},
  author = {Toshbuvayeva, Odinaxon},
  journal = {FarDU ilmiy xabarlari},
  year = {2026},
  volume = {7},
  number = {5},
  url = {https://journal.fdu.uz/main/article/7762}
}

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