DOAJ Open Access 2023

On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative

E.T. Karimov A. Hasanov

Abstrak

We aim to study a unique solvability of a boundary-value problem for a time-fractional diffusion equation involving the Prabhakar fractional derivative in a Caputo sense in a bounded domain. We use the method of separation of variables and in time-variable, we obtain the Cauchy problem for a fractional differential equation with the Prabhakar derivative. Solution of this Cauchy problem we represent via Mittag-Leffler type function of two variables. Using the new integral representation of this two-variable Mittag-Leffler type function, we obtained the required estimate, which allows us to prove uniform convergence of the infinite series form of the solution for the considered problem.

Topik & Kata Kunci

Analysis Analytic mechanics Probabilities. Mathematical statistics

Penulis (2)

E.T. Karimov

A. Hasanov

Format Sitasi

APA MLA BibTeX

Karimov, E., Hasanov, A. (2023). On a boundary-value problem in a bounded domain for a time-fractional diffusion equation with the Prabhakar fractional derivative. https://doi.org/10.31489/2023m3/39-46

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Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.31489/2023m3/39-46
Akses: Open Access ✓