INTEGRAL REPRESENTATION FOR HYPERGEOMETRIC FUNCTION OF THE MITTAG-LEFFLER TYPE

INTEGRAL REPRESENTATION FOR HYPERGEOMETRIC FUNCTION OF THE MITTAG-LEFFLER TYPE

Авторы

  • Hasanovich Mathematical Institute named after Romanovsky V.I
  • Yuldashovna Mathematical Institute named after Romanovsky V.I

DOI:

https://doi.org/10.52754/16948645_2023_2_220

Ключевые слова:

функция Миттаг-Леффлера, дифференциальные уравнения дробного порядка, интегральные уравнения дробного порядка

Аннотация

The Mittag-Leffler function has gained importance and popularity through its applications. When solving differential equations of fractional order and integral equations of fractional order. Also, the Mittag-Leffler function plays an important role in various fields of applied mathematics and engineering sciences, such as chemistry, biology, statistics, thermodynamics, mechanics, quantum physics, computer science, signal processing [1-6].

Библиографические ссылки

Mittag–Leffler GM. Sur la nouvelle fonction . C R Acad Sci Paris. 1903;137:554–558.

Luchko Y. Initial boundary value problems for the generalized multiterm time fractional

diffusion equation. J Math Anal Appl. 2011; 374: 538–548. DOI: https://doi.org/10.1016/j.jmaa.2010.08.048

Li Z, Liu Y, Yamamoto M. Initial boundary value problems for multi-term time-fractional

diffusion equations with positive constant coefficients. Appl Math Comput. 2015; 257:381–397. DOI: https://doi.org/10.1016/j.amc.2014.11.073

Salim T.O. Some properties relating to the generalized Mittage–Leffler function. Adv Appl Math Anal. 2009; 4:21–30.

Luchko Y, Gorenflo R. An operational method for solving fractional differential equations with the Caputo derivatives. Acta Math Vietnam. 1999; 24:207–233.

Gorenflo R, Kilbas A, Mainardi F, Rogosin S. Mittag-Leffler Functions, Related Topics and Applications. 2nd edition: Springer-Verlag GmbH Germany, 2020. DOI: https://doi.org/10.1007/978-3-662-61550-8

Srivastava H.M., Daoust Martha C. On Eulerian integrals associated with Kampe de Feriet’s function. Publications de L’institut Mathematique, Nouvelle serie, 1969, T. 9 (23), 199-202.

Maged G. Bin-Saad, Anvar Hasanov and Michael Ruzhansky (2021), Some properties relating to the Mittag–Leffler function of two variables. Integral Transforms and Special Functions. 2022, 33(5), pp. 400–418. DOI: https://doi.org/10.1080/10652469.2021.1939328

Загрузки

Опубликован

30-12-2023

Как цитировать

Hasanov, A., & Yuldashova, K. (2023). INTEGRAL REPRESENTATION FOR HYPERGEOMETRIC FUNCTION OF THE MITTAG-LEFFLER TYPE : INTEGRAL REPRESENTATION FOR HYPERGEOMETRIC FUNCTION OF THE MITTAG-LEFFLER TYPE . Вестник Ошского государственного университета. Математика. Физика. Техника, (2(3), 220–223. https://doi.org/10.52754/16948645_2023_2_220

Выпуск

№ 2(3) (2023): Вестник Ошского государственного университета. Математика. Физика. Техника

Раздел

МАТЕМАТИКА

Лицензия

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