In this paper, we aim to study the Cauchy problem posed for a fractional order equation. General solution of the time-fractional equation is found by the Fourier method. The solution to the given problem is shown to be unique using the generalized Hankel transform. The solution consists of the Bessel function and the Mittag-Leffler function. Unknown coefficients are found by Hankel transformation. It is shown that the constructed solution satisfies the initial condition and equation.
| Mualliflar | Hasanov, A., Yuldashova, H. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-6 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-6 · Maqolaning asl sahifasi
Cauchy problem, Riemann–Liouville fractional operator, Hankel transform, Mittag-Leffler function, Bessel function
| APA | Hasanov, A., & Yuldashova, H. (2026). Cauchy problem for fractional high order equation with singular coefficient. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-6 |
|---|---|
| GOST (OAK) | Hasanov, A., Yuldashova, H. Cauchy problem for fractional high order equation with singular coefficient // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-6. |
| MLA | Hasanov, A., and Yuldashova, H. “Cauchy problem for fractional high order equation with singular coefficient.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-6 |
| Chicago | Hasanov, A., and Yuldashova, H. “Cauchy problem for fractional high order equation with singular coefficient.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-6 |
| Harvard | Hasanov, A., and Yuldashova, H (2026) ‘Cauchy problem for fractional high order equation with singular coefficient’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-6 |
| BibTeX | @article{hasanova2026,
title = {Cauchy problem for fractional high order equation with singular coefficient},
author = {Hasanov, A. and Yuldashova, H.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-6},
url = {https://doi.org/10.29229/uzmj.2026-1-6}
} |
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