The first boundary value problem in a rectangular domain for a differential equation with the Bessel operator and the Riemann–Liouville partial derivative

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The paper is devoted to the first boundary-value problem in a rectangular domain for a differential equation with the singular Bessel operator acting with respect to a spatial variable and the Riemann–Liouville fractional differentiation operator acting with respect to a time variable. An explicit representation of the solution is constructed. The uniqueness of the solution is proved in the class of functions satisfying the Hölder condition with respect to the time variable. When the order of the fractional derivative is equal to unity, and the Bessel operator has no singularity, the studied equation coincides with the heat equation and the obtained results coincide with well-known corresponding classical results.

About the authors

Fatima G. Khushtova

Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS

Author for correspondence.
Email: khushtova@yandex.ru
ORCID iD: 0000-0003-4088-3621
SPIN-code: 6803-4959
Scopus Author ID: 57190074440
ResearcherId: K-1951-2018
http://www.mathnet.ru/person53181

Researcher; Dept. of Fractional Calculus

89 a, Shortanova st., Nal’chik, 360000, Russian Federation

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