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Ushbu maqolada Mittag-Leffler tipidagi funksiyalarning integral ko‘rinishlari topilgan. Bunda Eylerning gamma-funksiyasi xossalari hamda Rayt funksiyasining ayrim xossalaridan foydalanilgan.

  • Internet ҳавола
  • DOIhttps://doi.org/10.56292/SJFSU/vol28_iss6/a87
  • UzSCI тизимида яратилган сана 21-01-2023
  • Ўқишлар сони 330
  • Нашр санаси 15-12-2022
  • Мақола тилиO'zbek
  • Саҳифалар сони424-246
Ўзбек

Ushbu maqolada Mittag-Leffler tipidagi funksiyalarning integral ko‘rinishlari topilgan. Bunda Eylerning gamma-funksiyasi xossalari hamda Rayt funksiyasining ayrim xossalaridan foydalanilgan.

Русский

В Этой статье найдены интегральные представления функций типа Миттаг-Леффлера. При этом использованы свойства гамма-функции и функции Райта.

English

In this paper, integral representations of Mittag-Leffler type functions have been found using certain properties of gamma-function and Wright function.

№ Муаллифнинг исми Лавозими Ташкилот номи
1 Karimov E.. 1 Fergana State University
2 Maxkamov I.. 2 Fergana State University
№ Ҳавола номи
1 1. Uchaikin V.V. Fractional derivatives for physicists and engineers. Vol. I,II. Springer, Heidelberg, 2013.
2 2. Kilbas A.A, Srivastava H.M, Trujillo J.J. Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.
3 3. Podlubny I. Fractional differential equations. An introduction to fractional derivateves, fractional differential equations, to methods of their solution and some applications. Academic Press, San Diego, 1999.
4 4. Gorenflo R., Kilbas A. A., Mainardi F. Mittag-Leffler functions related topics and applications. Springer, Berlin, 2014.
5 5. Mainardi F., Pagnini G. The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Journal of Computational and Applied Mathematics, 2007,2, pp. 245-257.
6 6. Praphakar T.R. A singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama math. J. 1971, 19, pp. 7-15.
7 7. Pskhu A.V. Partial Differential Equations of Fractional Order. Nauka, Moscow, 2005.
8 8. Karimov E, Al-Salti N, Kerbal S. An inverse source non-local problem for a mixed type equation with a Caputo fractional differential operator. East Asian journal of Applied Mathematics, 2017, 2, pp. 417-438.
9 9. Salakhitdinov M.S, Karimov E.T. Direct and inverse source problems for two-term time fractional diffusion equation with Hilfer derivative. Uzbek Mathematical Journal, 2017, 4. pp. 140-149.
10 10. Karimov E.T, Kerbal S. Tricomi type problem for mixed type equation with sub-diffusion and wave equation. FDU. Ilmiy Khabarlar, 2019, 3, pp. 10-14.
11 11. Allen I.K, Doggal D, Nasir S, Karimov E. On a boundary value problem for a time- fractional wave equation with the Riemann-Liouville and Atangana-Baleanu derivatives. Bulletin of the Institute of Mathematics, 2020, 1, pp. 1-9.
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