Email this article 
ON THE SOLVABILITY OF THE CAUCHY PROBLEM IN GEVREY CLASSES FOR THE WEYL FRACTIONAL DERIVATIVE EQUATION
- Authors: Alimov S.A.1,2
-
Affiliations:
- National University of Uzbekistan named after Mirzo Ulugbek
- V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan
- Issue: Vol 523, No 1 (2025)
- Pages: 27-30
- Section: MATHEMATICS
- URL: https://ogarev-online.ru/2686-9543/article/view/305341
- DOI: https://doi.org/10.7868/S3034504925030055
- EDN: https://elibrary.ru/JSKIDW
- ID: 305341
Cite item
Open Access
Access granted
Subscription Access
Abstract
An alternative definition of fractional-order Weyl derivatives is given and their effect on functions from the Gevrey classes is studied. Conditions for the solvability of the Cauchy problem in Gevrey classes are found for the Weyl partial differential equation.
About the authors
S. A. Alimov
National University of Uzbekistan named after Mirzo Ulugbek; V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan
Email: sh_alimov@mail.ru
Tashkent, Uzbekistan
References
- Weyl H. Bemerkungen zum Begriff des Differentialquotienten gebrochener Ordnung // Vierteljahresschrift der Naturforschenden Gesellschaft in Zurich. 1917. Bd 62. № 1–2. P. 296–302.
- Samko St.G., Kilbas A.A., Marichev O.I. Fractional integrals and derivatives: theory and applications. New York, Gordon and Breach, 1993, 976 p.
- Гантьюкер Ф. Р. Теория матриц. Москва, Наука, 1967, 576 стр.
- Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations, Elsevier. 2006.
- Kirane M., Samet B., Torebek B.T. Determination of an unknown source term and the temperature distribution for the subdiffusion equation at the initial and final data // Journal of Differential Equations. 2017. V. 217. P. 1–13.
- Ashurov R.R., Shakarova M., Umarov S. An inverse problem for the subdiffusion equation with a non-local in time condition // Fractal Fract. 2024. № 8. P. 378.
- Hadamard J. Lectures on Cauchy’s problem in linear partial differential equations. New Haven: Yale University Press; London: Humphrey Milford; Oxford: University Press. VIII u. 316 S., 1923.
- Kabanikhin S.I. Inverse and Ill-posed Problems: Theory and Applications, Walter de Gruyter GmbH & Co. KG, Berlin/Boston, Inverse Ill-posed Probl. Ser. 55, 2012.
- Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Numerical Methods for the Solution of Ill-Posed Problems, Kluwer Academic Publishers, 1995.
- Ульянов П.Л. О классах бесконечно дифференцируемых функций // Докл. АН СССР. 1989. Т. 305. № 2. С. 287–290.
- Ульянов П.Л. О свойствах функций из классов Жевре // Докл. АН СССР. 1990. Т 314. № 4. С. 793–797.
- Ульянов П.Л. О классах бесконечно дифференцируемых функций // Матем. сб. 1990. Т. 181. № 5. С. 589–609.
- Kaxan Ж.П. Абсолютно сходящиеся ряды Фурье, М.: Мир, 1976.
- Хёрмандер Л. Анализ линейных дифференциальных операторов с частными производными, том 1, Теория распределений и анализ Фурье, М: Мир, 1986.
- Alimov S. A., Qudaybergenov A. K. Determination of temperature at the outer boundary of a body // Journal of Mathematical Sciences. 2023. V. 274. № 2. P. 159–171.
Supplementary files
Note
In the print version, the article was published under the DOI: 10.31857/S2686954325030055